Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations
A bstract Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized WDVV equations of [42]. We consider the Hurwitz p...
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| Abstract | A
bstract
Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized WDVV equations of [42]. We consider the Hurwitz partition functions, associated in this way with the CAA of cut-and-join operators. The ordinary Hurwitz numbers for a given number of sheets in the covering provide trivial (sums of exponentials) solutions to the WDVV equations, with finite number of time-variables. The generalized Hurwitz numbers from [32, 33] provide a non-trivial solution with infinite number of times. The simplest solution of this type is associated with a subring, generated by the dilatation operators
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| AbstractList | Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized WDVV equations of [42]. We consider the Hurwitz partition functions, associated in this way with the CAA of cut-and-join operators. The ordinary Hurwitz numbers for a given number of sheets in the covering provide trivial (sums of exponentials) solutions to the WDVV equations, with finite number of time-variables. The generalized Hurwitz numbers from [32, 33] provide a non-trivial solution with infinite number of times. The simplest solution of this type is associated with a subring, generated by the dilatation operators . A bstract Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized WDVV equations of [42]. We consider the Hurwitz partition functions, associated in this way with the CAA of cut-and-join operators. The ordinary Hurwitz numbers for a given number of sheets in the covering provide trivial (sums of exponentials) solutions to the WDVV equations, with finite number of time-variables. The generalized Hurwitz numbers from [32, 33] provide a non-trivial solution with infinite number of times. The simplest solution of this type is associated with a subring, generated by the dilatation operators . |
| ArticleNumber | 97 |
| Author | Morozov, A. Natanzon, S. Mironov, A. |
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| Cites_doi | 10.1023/A:1021791611677 10.1002/cpa.3160470403 10.1090/S0894-0347-07-00566-8 10.1016/j.geomphys.2010.10.017 10.1007/s002200050427 10.1088/1126-6708/2009/04/064 10.1007/s002220100164 10.1007/s11232-011-0001-6 10.1007/BF01448116 10.1016/0550-3213(92)90137-Z 10.1007/PL00001274 10.1007/BF02465202 10.1007/BF02099016 10.1016/S0550-3213(98)00315-0 10.1070/IM2004v068n05ABEH000504 10.1070/RM2002v057n03ABEH000511 10.1016/j.geomphys.2011.09.001 10.1016/S0040-9383(98)00036-6 10.1201/9780203885765.ch7 10.1007/BF01199469 10.1023/A:1012473607966 10.1016/0550-3213(91)90129-L 10.1090/S0002-9939-97-03880-X 10.4007/annals.2006.163.517 10.1088/1126-6708/2009/02/024 10.4310/MRL.2000.v7.n4.a10 10.1142/S0217751X9500098X 10.1016/S0370-2693(01)00893-0 10.1142/S0217732311036607 10.4310/SDG.1990.v1.n1.a5 10.1090/pspum/078/2483754 10.1016/S0375-9601(99)00500-9 10.1142/S0217732309031995 10.1007/978-1-4612-4264-2_5 10.1093/oso/9780198534891.001.0001 10.1142/S0217732397000807 10.1142/S0217751X00000537 10.1016/S0370-2693(96)01231-2 10.1016/S0370-2693(98)00150-6 10.1090/trans2/224/01 10.1007/s00029-006-0028-y |
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| References | Lando, Zvonkine (CR7) 1999; 33 Goulden, Jackson (CR6) 1997; 125 Marshakov, Mironov, Morozov (CR42) 1996; B 389 Lechtenfeld, Schwerdtfeger, Thürigen (CR60) 2011; 7 Lando, Koolen, Kwak, Xu (CR25) 2008 CR34 Alexeevski, Natanzon (CR15) 2006; 12 Hurwitz (CR2) 1902; 55 Veselov (CR58) 1999; A 261 Mironov, Morozov (CR27) 2009; 02 CR4 CR3 Natanzon (CR16) 2006; 61 Fulton (CR37) 1997 Mironov, Morozov (CR56) 1998; B 424 CR5 CR8 Mironov, Morozov, Natanzon (CR32) 2011; 166 Witten (CR48) 1991; 1 CR47 Kharchev, Marshakov, Mironov, Morozov (CR61) 1995; A 10 Morozov, Shakirov (CR29) 2009; A 24 CR41 Alexeevski, Natanzon (CR18) 2008; 224 Hurwitz (CR1) 1891; 39 Kazarian, Lando (CR23) 2007; 20 Okounkov (CR11) 2000; 7 Littlewood (CR35) 1958 Krichever (CR50) 1994; 47 CR19 CR17 CR59 CR12 Lando (CR14) 2002; 57 CR52 Hamermesh (CR38) 1989 Okounkov, Olshanski (CR40) 1998; 9 Boyarsky, Marshakov, Ruchayskiy, Wiegmann, Zabrodin (CR46) 2001; B 515 Dubrovin (CR51) 1992; B 379 Borot, Eynard, Mulase, Safnuk (CR30) 2011; 61 Marshakov, Mironov, Morozov (CR55) 1997; A 12 Mironov, Braden, Krichever (CR57) 2000 Dijkgraaf, Verlinde, Verlinde (CR49) 1991; B 352 Gorsky, Marshakov, Mironov, Morozov (CR45) 1998; B 527 Krichever (CR44) 1992; 143 Goulden, Jackson, Vainshtein (CR10) 2000; 4 Krichever (CR43) 1994; 47 Macdonald (CR36) 1995 Okounkov, Pandharipande (CR20) 2006; 163 Ekedahl, Lando, Shapiro, Vainshtein (CR13) 2001; 146 Natanzon, Turaev (CR53) 1998; 196 CR26 CR24 Graber, Vakil (CR21) 2003; 135 Mironov, Morozov, Natanzon (CR33) 2012; 62 Morozov, Shakirov (CR28) 2009; 04 Marshakov, Mironov, Morozov (CR54) 2000; A 15 Kazaryan, Lando (CR22) 2004; 68 Alexandrov (CR31) 2011; A 26 Ivanov, Kerov (CR39) 2001; 107 Natanzon, Turaev (CR9) 1999; 38 3058_CR12 I Krichever (3058_CR50) 1994; 47 W Fulton (3058_CR37) 1997 3058_CR52 SM Natanzon (3058_CR16) 2006; 61 B Dubrovin (3058_CR51) 1992; B 379 A Marshakov (3058_CR54) 2000; A 15 S Kharchev (3058_CR61) 1995; A 10 3058_CR8 A Morozov (3058_CR29) 2009; A 24 T Graber (3058_CR21) 2003; 135 3058_CR19 3058_CR17 S Natanzon (3058_CR53) 1998; 196 3058_CR3 IP Goulden (3058_CR6) 1997; 125 3058_CR59 I Krichever (3058_CR44) 1992; 143 3058_CR5 3058_CR4 3058_CR41 S Natanzon (3058_CR9) 1999; 38 A Veselov (3058_CR58) 1999; A 261 A Okounkov (3058_CR20) 2006; 163 S Lando (3058_CR25) 2008 T Ekedahl (3058_CR13) 2001; 146 ME Kazaryan (3058_CR22) 2004; 68 A Morozov (3058_CR28) 2009; 04 G Borot (3058_CR30) 2011; 61 A Mironov (3058_CR33) 2012; 62 O Lechtenfeld (3058_CR60) 2011; 7 IG Macdonald (3058_CR36) 1995 V Ivanov (3058_CR39) 2001; 107 A Alexeevski (3058_CR18) 2008; 224 3058_CR47 3058_CR34 A Alexandrov (3058_CR31) 2011; A 26 DE Littlewood (3058_CR35) 1958 A Mironov (3058_CR56) 1998; B 424 A Mironov (3058_CR57) 2000 M Hamermesh (3058_CR38) 1989 A Mironov (3058_CR32) 2011; 166 A Marshakov (3058_CR55) 1997; A 12 A Marshakov (3058_CR42) 1996; B 389 A Boyarsky (3058_CR46) 2001; B 515 A Mironov (3058_CR27) 2009; 02 E Witten (3058_CR48) 1991; 1 A Okounkov (3058_CR11) 2000; 7 D Goulden (3058_CR10) 2000; 4 R Dijkgraaf (3058_CR49) 1991; B 352 A Hurwitz (3058_CR2) 1902; 55 S Lando (3058_CR7) 1999; 33 A Hurwitz (3058_CR1) 1891; 39 A Gorsky (3058_CR45) 1998; B 527 I Krichever (3058_CR43) 1994; 47 ME Kazarian (3058_CR23) 2007; 20 S Lando (3058_CR14) 2002; 57 3058_CR26 3058_CR24 A Alexeevski (3058_CR15) 2006; 12 A Okounkov (3058_CR40) 1998; 9 |
| References_xml | – volume: 135 start-page: 25 year: 2003 ident: CR21 article-title: Hodge integrals and Hirwitz numbers via virtual localization publication-title: Compos. Math. doi: 10.1023/A:1021791611677 – volume: 47 start-page: 437 year: 1994 ident: CR43 article-title: The τ function of the universal Whitham hierarchy, matrix models and topological field theories publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160470403 – volume: B 424 start-page: 48 year: 1998 ident: CR56 article-title: Covariance of WDVV equations publication-title: Phys. Lett. – volume: 20 start-page: 1079 year: 2007 ident: CR23 article-title: An algebro-geometric proof of Witten’s conjecture publication-title: J. Amer. Math. Soc. doi: 10.1090/S0894-0347-07-00566-8 – ident: CR4 – volume: 12 start-page: 307 year: 2006 ident: CR15 article-title: Noncommutative extensions of two-dimensional topological field theories and Hurwitz numbers for real algebraic curves publication-title: Selecta Math. – ident: CR12 – volume: 61 start-page: 522 year: 2011 ident: CR30 article-title: A matrix model for simple Hurwitz numbers and topological recursion publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2010.10.017 – volume: 61 start-page: 185 year: 2006 ident: CR16 article-title: Algebra of Hurwitz numbers for seamed surfaces publication-title: Russ. Math. Surv. – volume: B 389 start-page: 43 year: 1996 ident: CR42 article-title: WDVV-like equations in N = 2 SUSY Yang-Mills theory publication-title: Phys. Lett. – volume: 196 start-page: 399 year: 1998 ident: CR53 article-title: Systems of correlators and solutions of the WDVV equations publication-title: Commun. Math. Phys. doi: 10.1007/s002200050427 – volume: A 12 start-page: 773 year: 1997 ident: CR55 article-title: WDVV equations from algebra of forms publication-title: Mod. Phys. Lett. – ident: CR8 – volume: 47 start-page: 437 year: 1994 ident: CR50 article-title: The τ -function of the universal Whitham hierarchy, matrix models and topological field theories publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160470403 – year: 1989 ident: CR38 publication-title: Group theory and its application to physical problems – volume: 04 start-page: 064 year: 2009 ident: CR28 article-title: Generation of matrix models by Ŵ-operators publication-title: JHEP doi: 10.1088/1126-6708/2009/04/064 – volume: 9 start-page: 2 year: 1998 ident: CR40 article-title: Shifted Schur functions publication-title: St. Petersburg Math. J. – volume: 7 start-page: 023 year: 2011 ident: CR60 article-title: N = 4 multi-particle mechanics, WDVV equation and roots publication-title: SIGMA – ident: CR19 – volume: 146 start-page: 297 year: 2001 ident: CR13 article-title: Hurwitz numbers and intersections on moduli spaces of curves publication-title: Invent. Math. doi: 10.1007/s002220100164 – year: 1995 ident: CR36 publication-title: Symmetric functions and Hall polynomials – volume: 166 start-page: 1 year: 2011 ident: CR32 article-title: Complete set of cut-and-join operators in Hurwitz-Kontsevich theory publication-title: Theor. Math. Phys. doi: 10.1007/s11232-011-0001-6 – volume: A 15 start-page: 1157 year: 2000 ident: CR54 article-title: More evidence for the WDVV equations in N = 2 SUSY Yang-Mills theories publication-title: Int. J. Mod. Phys. – volume: 55 start-page: 53 year: 1902 ident: CR2 article-title: Über die Anzal der Riemann’sche Flächen mit gegebenen Verzweigungpunkten (in German) publication-title: Math. Ann. doi: 10.1007/BF01448116 – volume: 7 start-page: 447 year: 2000 ident: CR11 article-title: Toda equations for Hurwitz numbers publication-title: Math. Res. Lett. – volume: B 379 start-page: 627 year: 1992 ident: CR51 article-title: Integrable systems in topological field theory publication-title: Nucl. Phys. doi: 10.1016/0550-3213(92)90137-Z – volume: B 515 start-page: 483 year: 2001 ident: CR46 article-title: On associativity equations in dispersionless integrable hierarchies publication-title: Phys. Lett. – volume: 4 start-page: 27 year: 2000 ident: CR10 article-title: The number of ramifified coverings of the sphere by torus and surfaces of higher genera publication-title: Ann. Comb. doi: 10.1007/PL00001274 – volume: 33 start-page: 178 year: 1999 ident: CR7 article-title: On multiplicitites of the Lyashko-Looijenga mapping on the discriminant strata publication-title: Funct. Anal. Appl. doi: 10.1007/BF02465202 – ident: CR5 – volume: 143 start-page: 415 year: 1992 ident: CR44 article-title: The dispersionless Lax equations and topological minimal models publication-title: Commun. Math. Phys. doi: 10.1007/BF02099016 – volume: B 527 start-page: 690 year: 1998 ident: CR45 article-title: RG equations from Whitham hierarchy publication-title: Nucl. Phys. doi: 10.1016/S0550-3213(98)00315-0 – ident: CR26 – volume: A 10 start-page: 2015 year: 1995 ident: CR61 article-title: Generalized Kazakov-Migdal-Kontsevich model: group theory aspects publication-title: Int. J. Mod. Phys. – volume: 68 start-page: 935 year: 2004 ident: CR22 article-title: Towards an intersection theory on Hurwitz spaces publication-title: Izv. Math. doi: 10.1070/IM2004v068n05ABEH000504 – volume: 57 start-page: 463 year: 2002 ident: CR14 article-title: Ramified coverings of the two-dimensional sphere and intersection theory in spaces of meromorphic functions on algebraic curves publication-title: Russ. Math. Surv. doi: 10.1070/RM2002v057n03ABEH000511 – volume: 62 start-page: 148 year: 2012 ident: CR33 article-title: Algebra of differential operators associated with Young diagrams publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2011.09.001 – volume: 38 start-page: 889 year: 1999 ident: CR9 article-title: A compactification of Hurwitz space publication-title: Topology doi: 10.1016/S0040-9383(98)00036-6 – ident: CR47 – start-page: 109 year: 2008 ident: CR25 article-title: Combinatorial facets of Hurwitz numbers publication-title: Applications of group theory to combinatorics doi: 10.1201/9780203885765.ch7 – volume: 39 start-page: 1 year: 1891 ident: CR1 article-title: Über Riemann’sche Flächen mit gegebenen Verzweigungpunkten (in German) publication-title: Math. Ann. doi: 10.1007/BF01199469 – volume: A 24 start-page: 2659 year: 2009 ident: CR29 article-title: On equivalence of two Hurwitz matrix models publication-title: Mod. Phys. Lett. – year: 1997 ident: CR37 publication-title: Young tableaux: with applications to representation theory and geometry – year: 2000 ident: CR57 article-title: WDVV equations and Seiberg-Witten theory publication-title: Integrability: the Seiberg-Witten and Whitham equations – volume: 107 start-page: 4212 year: 2001 ident: CR39 article-title: The algebra of conjugacy classes in symmetric groups and partial permutations publication-title: J. Math. Sci. doi: 10.1023/A:1012473607966 – volume: 224 start-page: 1 year: 2008 ident: CR18 article-title: Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebra of finite groups publication-title: Amer. Math. Soc. Transl. – volume: A 26 start-page: 2193 year: 2011 ident: CR31 article-title: Cut-and-join operator representation for Kontsewich-Witten τ -function publication-title: Mod. Phys. Lett. – year: 1958 ident: CR35 publication-title: The theory of group characters and matrix representations of groups – volume: B 352 start-page: 59 year: 1991 ident: CR49 article-title: Topological strings in d < 1 publication-title: Nucl. Phys. doi: 10.1016/0550-3213(91)90129-L – volume: 125 start-page: 51 year: 1997 ident: CR6 article-title: Transitive factorisations in the symmetric group and combinatorial aspects of singularity theory publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-97-03880-X – ident: CR3 – volume: 1 start-page: 243 year: 1991 ident: CR48 article-title: Two-dimensional gravity and intersection theory on moduli space publication-title: Surv. Diff. Geom. – ident: CR52 – ident: CR17 – volume: A 261 start-page: 297 year: 1999 ident: CR58 article-title: Deformations of the root systems and new solutions to generalized WDVV equations publication-title: Phys. Lett. – ident: CR34 – ident: CR59 – volume: 163 start-page: 517 year: 2006 ident: CR20 article-title: Gromov-Witten theory, Hurwitz theory and completed cycles publication-title: Ann. Math. doi: 10.4007/annals.2006.163.517 – ident: CR41 – ident: CR24 – volume: 02 start-page: 024 year: 2009 ident: CR27 article-title: Virasoro constraints for Kontsevich-Hurwitz partition function publication-title: JHEP doi: 10.1088/1126-6708/2009/02/024 – ident: 3058_CR17 – volume-title: Young tableaux: with applications to representation theory and geometry year: 1997 ident: 3058_CR37 – volume: 196 start-page: 399 year: 1998 ident: 3058_CR53 publication-title: Commun. Math. Phys. doi: 10.1007/s002200050427 – ident: 3058_CR3 – volume: 38 start-page: 889 year: 1999 ident: 3058_CR9 publication-title: Topology doi: 10.1016/S0040-9383(98)00036-6 – volume-title: The theory of group characters and matrix representations of groups year: 1958 ident: 3058_CR35 – volume: 163 start-page: 517 year: 2006 ident: 3058_CR20 publication-title: Ann. Math. doi: 10.4007/annals.2006.163.517 – start-page: 109 volume-title: Applications of group theory to combinatorics year: 2008 ident: 3058_CR25 doi: 10.1201/9780203885765.ch7 – volume: 68 start-page: 935 year: 2004 ident: 3058_CR22 publication-title: Izv. Math. doi: 10.1070/IM2004v068n05ABEH000504 – volume: 04 start-page: 064 year: 2009 ident: 3058_CR28 publication-title: JHEP doi: 10.1088/1126-6708/2009/04/064 – volume: 7 start-page: 447 year: 2000 ident: 3058_CR11 publication-title: Math. Res. Lett. doi: 10.4310/MRL.2000.v7.n4.a10 – volume: A 10 start-page: 2015 year: 1995 ident: 3058_CR61 publication-title: Int. J. Mod. Phys. doi: 10.1142/S0217751X9500098X – ident: 3058_CR52 – volume: B 515 start-page: 483 year: 2001 ident: 3058_CR46 publication-title: Phys. Lett. doi: 10.1016/S0370-2693(01)00893-0 – volume: A 26 start-page: 2193 year: 2011 ident: 3058_CR31 publication-title: Mod. Phys. Lett. doi: 10.1142/S0217732311036607 – volume-title: Integrability: the Seiberg-Witten and Whitham equations year: 2000 ident: 3058_CR57 – ident: 3058_CR47 – volume: 1 start-page: 243 year: 1991 ident: 3058_CR48 publication-title: Surv. Diff. Geom. doi: 10.4310/SDG.1990.v1.n1.a5 – ident: 3058_CR26 doi: 10.1090/pspum/078/2483754 – ident: 3058_CR8 – volume: 4 start-page: 27 year: 2000 ident: 3058_CR10 publication-title: Ann. Comb. doi: 10.1007/PL00001274 – volume: 39 start-page: 1 year: 1891 ident: 3058_CR1 publication-title: Math. Ann. doi: 10.1007/BF01199469 – volume: 47 start-page: 437 year: 1994 ident: 3058_CR50 publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160470403 – volume: A 261 start-page: 297 year: 1999 ident: 3058_CR58 publication-title: Phys. Lett. doi: 10.1016/S0375-9601(99)00500-9 – ident: 3058_CR19 – volume: 125 start-page: 51 year: 1997 ident: 3058_CR6 publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-97-03880-X – volume: A 24 start-page: 2659 year: 2009 ident: 3058_CR29 publication-title: Mod. Phys. Lett. doi: 10.1142/S0217732309031995 – ident: 3058_CR4 doi: 10.1007/978-1-4612-4264-2_5 – volume: 9 start-page: 2 year: 1998 ident: 3058_CR40 publication-title: St. Petersburg Math. J. – volume: 7 start-page: 023 year: 2011 ident: 3058_CR60 publication-title: SIGMA – volume-title: Symmetric functions and Hall polynomials year: 1995 ident: 3058_CR36 doi: 10.1093/oso/9780198534891.001.0001 – volume: B 352 start-page: 59 year: 1991 ident: 3058_CR49 publication-title: Nucl. Phys. doi: 10.1016/0550-3213(91)90129-L – ident: 3058_CR5 – volume: 02 start-page: 024 year: 2009 ident: 3058_CR27 publication-title: JHEP doi: 10.1088/1126-6708/2009/02/024 – volume: 62 start-page: 148 year: 2012 ident: 3058_CR33 publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2011.09.001 – volume: 55 start-page: 53 year: 1902 ident: 3058_CR2 publication-title: Math. Ann. doi: 10.1007/BF01448116 – volume: A 12 start-page: 773 year: 1997 ident: 3058_CR55 publication-title: Mod. Phys. Lett. doi: 10.1142/S0217732397000807 – volume: 166 start-page: 1 year: 2011 ident: 3058_CR32 publication-title: Theor. Math. Phys. doi: 10.1007/s11232-011-0001-6 – volume: 47 start-page: 437 year: 1994 ident: 3058_CR43 publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160470403 – volume: 146 start-page: 297 year: 2001 ident: 3058_CR13 publication-title: Invent. Math. doi: 10.1007/s002220100164 – ident: 3058_CR12 – volume: 61 start-page: 185 year: 2006 ident: 3058_CR16 publication-title: Russ. Math. Surv. – volume: B 527 start-page: 690 year: 1998 ident: 3058_CR45 publication-title: Nucl. Phys. doi: 10.1016/S0550-3213(98)00315-0 – volume: 135 start-page: 25 year: 2003 ident: 3058_CR21 publication-title: Compos. Math. doi: 10.1023/A:1021791611677 – volume: A 15 start-page: 1157 year: 2000 ident: 3058_CR54 publication-title: Int. J. Mod. Phys. doi: 10.1142/S0217751X00000537 – ident: 3058_CR41 – volume: 143 start-page: 415 year: 1992 ident: 3058_CR44 publication-title: Commun. Math. Phys. doi: 10.1007/BF02099016 – volume: 61 start-page: 522 year: 2011 ident: 3058_CR30 publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2010.10.017 – ident: 3058_CR24 – volume: B 379 start-page: 627 year: 1992 ident: 3058_CR51 publication-title: Nucl. Phys. doi: 10.1016/0550-3213(92)90137-Z – volume: 33 start-page: 178 year: 1999 ident: 3058_CR7 publication-title: Funct. Anal. Appl. doi: 10.1007/BF02465202 – volume: B 389 start-page: 43 year: 1996 ident: 3058_CR42 publication-title: Phys. Lett. doi: 10.1016/S0370-2693(96)01231-2 – volume: B 424 start-page: 48 year: 1998 ident: 3058_CR56 publication-title: Phys. Lett. doi: 10.1016/S0370-2693(98)00150-6 – volume: 20 start-page: 1079 year: 2007 ident: 3058_CR23 publication-title: J. Amer. Math. Soc. doi: 10.1090/S0894-0347-07-00566-8 – volume-title: Group theory and its application to physical problems year: 1989 ident: 3058_CR38 – volume: 224 start-page: 1 year: 2008 ident: 3058_CR18 publication-title: Amer. Math. Soc. Transl. doi: 10.1090/trans2/224/01 – ident: 3058_CR59 – volume: 57 start-page: 463 year: 2002 ident: 3058_CR14 publication-title: Russ. Math. Surv. doi: 10.1070/RM2002v057n03ABEH000511 – ident: 3058_CR34 – volume: 12 start-page: 307 year: 2006 ident: 3058_CR15 publication-title: Selecta Math. doi: 10.1007/s00029-006-0028-y – volume: 107 start-page: 4212 year: 2001 ident: 3058_CR39 publication-title: J. Math. Sci. doi: 10.1023/A:1012473607966 |
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bstract
Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra... Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a... |
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| SubjectTerms | Chemical partition Classical and Quantum Gravitation Correlators Elementary Particles High energy physics Mathematical analysis Multiplication Operators (mathematics) Partitions (mathematics) Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Relativity Theory String Theory Topology |
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| Title | Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations |
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