The Bloch–Okounkov correlation functions of negative levels
Bloch and Okounkov introduced an n-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function affords several distinguished interpretations and in particular can be formulated as correlation functions on irreducible gl ˆ ∞ -modules of...
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| Vydáno v: | Journal of algebra Ročník 319; číslo 1; s. 457 - 490 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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2008
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| ISSN: | 0021-8693, 1090-266X |
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| Abstract | Bloch and Okounkov introduced an
n-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function affords several distinguished interpretations and in particular can be formulated as correlation functions on irreducible
gl
ˆ
∞
-modules of level one. These correlation functions have been generalized for irreducible integrable modules of
gl
ˆ
∞
and its classical Lie subalgebras of positive levels by the authors. In this paper we extend further these results and compute the correlation functions as well as the
q-dimensions for modules of
gl
ˆ
∞
and its classical subalgebras at negative levels. |
|---|---|
| AbstractList | Bloch and Okounkov introduced an
n-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function affords several distinguished interpretations and in particular can be formulated as correlation functions on irreducible
gl
ˆ
∞
-modules of level one. These correlation functions have been generalized for irreducible integrable modules of
gl
ˆ
∞
and its classical Lie subalgebras of positive levels by the authors. In this paper we extend further these results and compute the correlation functions as well as the
q-dimensions for modules of
gl
ˆ
∞
and its classical subalgebras at negative levels. |
| Author | Taylor, David G. Cheng, Shun-Jen Wang, Weiqiang |
| Author_xml | – sequence: 1 givenname: Shun-Jen surname: Cheng fullname: Cheng, Shun-Jen email: chengsj@math.sinica.edu.tw organization: Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan – sequence: 2 givenname: David G. surname: Taylor fullname: Taylor, David G. email: taylor@roanoke.edu organization: Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA – sequence: 3 givenname: Weiqiang surname: Wang fullname: Wang, Weiqiang email: ww9c@virginia.edu organization: Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA |
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| Cites_doi | 10.1006/aima.1999.1845 10.1142/S0219199799000080 10.1007/s00031-004-7006-2 10.1103/PhysRevD.39.2971 10.1007/PL00001398 10.1016/0167-2789(82)90041-0 10.1090/S0002-9947-1989-0986027-X 10.1016/S0022-4049(03)00036-7 10.1007/BF02100281 10.1016/0001-8708(85)90027-1 10.1007/s00031-004-7008-0 10.1007/s00220-007-0344-x 10.1006/aima.1998.1753 10.1007/BF02587735 10.1143/JPSJ.50.3806 |
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| Keywords | Representations at negative levels Infinite-dimensional Lie algebras Correlation functions q-dimension formulas |
| Language | English |
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Transformation groups for soliton equations III publication-title: J. Phys. Soc. Japan doi: 10.1143/JPSJ.50.3806 |
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| Snippet | Bloch and Okounkov introduced an
n-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function... |
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| SubjectTerms | Correlation functions Infinite-dimensional Lie algebras q-dimension formulas Representations at negative levels |
| Title | The Bloch–Okounkov correlation functions of negative levels |
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