The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and U(sl2)
The adjacency matrix of a symplectic dual polar graph restricted to the eigenspaces of an abelian automorphism subgroup is shown to act as the adjacency matrix of a weighted subspace lattice. The connection between the latter and Uq(sl2) is used to find the irreducible components of the standard mod...
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| Published in: | Discrete mathematics Vol. 345; no. 12; p. 113169 |
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| Format: | Journal Article |
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01.12.2022
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| Abstract | The adjacency matrix of a symplectic dual polar graph restricted to the eigenspaces of an abelian automorphism subgroup is shown to act as the adjacency matrix of a weighted subspace lattice. The connection between the latter and Uq(sl2) is used to find the irreducible components of the standard module of the Terwilliger algebra of symplectic dual polar graphs. The multiplicities of the isomorphic submodules are given. |
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| AbstractList | The adjacency matrix of a symplectic dual polar graph restricted to the eigenspaces of an abelian automorphism subgroup is shown to act as the adjacency matrix of a weighted subspace lattice. The connection between the latter and Uq(sl2) is used to find the irreducible components of the standard module of the Terwilliger algebra of symplectic dual polar graphs. The multiplicities of the isomorphic submodules are given. |
| ArticleNumber | 113169 |
| Author | Crampé, Nicolas Vinet, Luc Bernard, Pierre-Antoine |
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| Cites_doi | 10.1023/A:1022494701663 10.1016/j.laa.2013.09.050 10.1016/j.disc.2020.112018 10.1016/j.ejc.2004.08.005 10.2307/2374091 10.1016/j.disc.2006.09.012 10.1080/00029890.1969.12000160 10.1016/S0377-0427(02)00600-3 10.1023/A:1022415825656 10.1016/j.laa.2012.08.016 10.1016/j.laa.2020.03.005 10.1016/j.laa.2015.01.012 10.1137/0513044 10.1007/s00373-016-1744-5 10.1006/eujc.2000.0514 10.1023/A:1022480715311 10.1016/j.nuclphysb.2020.115176 10.1016/j.ejc.2018.02.029 10.1016/j.jalgebra.2017.06.033 |
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| Keywords | Dual polar graphs Terwilliger algebra quantum groups |
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| References | Terwilliger (10.1016/j.disc.2022.113169_br0230) 1990; vol. 20 Brouwer (10.1016/j.disc.2022.113169_br0040) 1989 Stanton (10.1016/j.disc.2022.113169_br0210) 1980; 102 Klimyk (10.1016/j.disc.2022.113169_br0110) 1997 Levstein (10.1016/j.disc.2022.113169_br0150) 2006; 27 Terwilliger (10.1016/j.disc.2022.113169_br0260) 1993; 2 Gao (10.1016/j.disc.2022.113169_br0080) 2015; 471 Schmidt (10.1016/j.disc.2022.113169_br0200) 1976 Terwilliger (10.1016/j.disc.2022.113169_br0270) 2003; 153 Bernard (10.1016/j.disc.2022.113169_br0020) Bernard (10.1016/j.disc.2022.113169_br0030) Huang (10.1016/j.disc.2022.113169_br0100) Liang (10.1016/j.disc.2022.113169_br0160) 2020; 596 Go (10.1016/j.disc.2022.113169_br0090) 2002; 23 Watanabe (10.1016/j.disc.2022.113169_br0280) 2017; 489 Bannai (10.1016/j.disc.2022.113169_br0010) 1984 Terwilliger (10.1016/j.disc.2022.113169_br0240) 1992; 1 Chan (10.1016/j.disc.2022.113169_br0050) 2020; 343 Terwilliger (10.1016/j.disc.2022.113169_br0250) 1993; 2 MacWilliams (10.1016/j.disc.2022.113169_br0180) 1969; 76 Rudolf (10.1016/j.disc.2022.113169_br0190) 1997 Crampé (10.1016/j.disc.2022.113169_br0060) 2020; 960 Leonard (10.1016/j.disc.2022.113169_br0130) 1982; 13 Gao (10.1016/j.disc.2022.113169_br0070) 2014; 443 Koekoek (10.1016/j.disc.2022.113169_br0120) 1998 Liang (10.1016/j.disc.2022.113169_br0170) 2017; 33 Worawannotai (10.1016/j.disc.2022.113169_br0290) 2013; 438 Levstein (10.1016/j.disc.2022.113169_br0140) 2007; 307 Tan (10.1016/j.disc.2022.113169_br0220) 2019; 80 |
| References_xml | – year: 1976 ident: 10.1016/j.disc.2022.113169_br0200 – volume: 1 start-page: 363 issue: 4 year: 1992 ident: 10.1016/j.disc.2022.113169_br0240 article-title: The subconstituent algebra of an association scheme (Part I) publication-title: J. Algebraic Comb. doi: 10.1023/A:1022494701663 – ident: 10.1016/j.disc.2022.113169_br0020 – volume: 443 start-page: 164 year: 2014 ident: 10.1016/j.disc.2022.113169_br0070 article-title: The Terwilliger algebras of Johnson graphs publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2013.09.050 – ident: 10.1016/j.disc.2022.113169_br0030 – volume: 343 issue: 11 year: 2020 ident: 10.1016/j.disc.2022.113169_br0050 article-title: Fractional revival and association schemes publication-title: Discrete Math. doi: 10.1016/j.disc.2020.112018 – year: 1998 ident: 10.1016/j.disc.2022.113169_br0120 – volume: 27 start-page: 1 issue: 1 year: 2006 ident: 10.1016/j.disc.2022.113169_br0150 article-title: The Terwilliger algebra of a Hamming scheme H(d,q) publication-title: Eur. J. Comb. doi: 10.1016/j.ejc.2004.08.005 – volume: 102 start-page: 625 issue: 4 year: 1980 ident: 10.1016/j.disc.2022.113169_br0210 article-title: Some q-Krawtchouk polynomials on Chevalley groups publication-title: Am. J. Math. doi: 10.2307/2374091 – volume: 307 start-page: 1621 issue: 13 year: 2007 ident: 10.1016/j.disc.2022.113169_br0140 article-title: The Terwilliger algebra of the Johnson schemes publication-title: Discrete Math. doi: 10.1016/j.disc.2006.09.012 – volume: 76 start-page: 152 issue: 2 year: 1969 ident: 10.1016/j.disc.2022.113169_br0180 article-title: Orthogonal matrices over finite fields publication-title: Am. Math. Mon. doi: 10.1080/00029890.1969.12000160 – volume: 153 start-page: 463 issue: 1 year: 2003 ident: 10.1016/j.disc.2022.113169_br0270 article-title: Introduction to Leonard pairs publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(02)00600-3 – volume: 2 start-page: 177 issue: 2 year: 1993 ident: 10.1016/j.disc.2022.113169_br0260 article-title: The subconstituent algebra of an association scheme (Part III) publication-title: J. Algebraic Comb. doi: 10.1023/A:1022415825656 – volume: vol. 20 start-page: 193 year: 1990 ident: 10.1016/j.disc.2022.113169_br0230 article-title: The incidence algebra of a uniform poset – volume: 438 start-page: 443 issue: 1 year: 2013 ident: 10.1016/j.disc.2022.113169_br0290 article-title: Dual polar graphs, the quantum algebra Uq(sl2), and Leonard systems of dual q-Krawtchouk type publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2012.08.016 – volume: 596 start-page: 117 year: 2020 ident: 10.1016/j.disc.2022.113169_br0160 article-title: The Terwilliger algebra of the Grassmann scheme Jq(n,d) revisited from the viewpoint of the quantum affine algebra Uq(sl2) publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2020.03.005 – year: 1984 ident: 10.1016/j.disc.2022.113169_br0010 – start-page: 20 year: 1997 ident: 10.1016/j.disc.2022.113169_br0190 – volume: 471 start-page: 427 year: 2015 ident: 10.1016/j.disc.2022.113169_br0080 article-title: The Terwilliger algebras of Grassmann graphs publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2015.01.012 – ident: 10.1016/j.disc.2022.113169_br0100 – volume: 13 start-page: 656 issue: 4 year: 1982 ident: 10.1016/j.disc.2022.113169_br0130 article-title: Orthogonal polynomials, duality and association schemes publication-title: SIAM J. Math. Anal. doi: 10.1137/0513044 – volume: 33 start-page: 149 issue: 1 year: 2017 ident: 10.1016/j.disc.2022.113169_br0170 article-title: An observation on Leonard system parameters for the Terwilliger algebra of the Johnson scheme J(N, D) publication-title: Graphs Comb. doi: 10.1007/s00373-016-1744-5 – year: 1997 ident: 10.1016/j.disc.2022.113169_br0110 – volume: 23 start-page: 399 issue: 4 year: 2002 ident: 10.1016/j.disc.2022.113169_br0090 article-title: The Terwilliger algebra of the hypercube publication-title: Eur. J. Comb. doi: 10.1006/eujc.2000.0514 – volume: 2 start-page: 73 issue: 1 year: 1993 ident: 10.1016/j.disc.2022.113169_br0250 article-title: The subconstituent algebra of an association scheme (Part II) publication-title: J. Algebraic Comb. doi: 10.1023/A:1022480715311 – volume: 960 year: 2020 ident: 10.1016/j.disc.2022.113169_br0060 article-title: Entanglement of free fermions on Hadamard graphs publication-title: Nucl. Phys. B doi: 10.1016/j.nuclphysb.2020.115176 – year: 1989 ident: 10.1016/j.disc.2022.113169_br0040 – volume: 80 start-page: 157 year: 2019 ident: 10.1016/j.disc.2022.113169_br0220 article-title: The Terwilliger algebra of the Johnson scheme J(N,D) revisited from the viewpoint of group representations publication-title: Eur. J. Comb. doi: 10.1016/j.ejc.2018.02.029 – volume: 489 start-page: 475 year: 2017 ident: 10.1016/j.disc.2022.113169_br0280 article-title: An algebra associated with a subspace lattice over a finite field and its relation to the quantum affine algebra Uq(sl2) publication-title: J. Algebra doi: 10.1016/j.jalgebra.2017.06.033 |
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