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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Vydáno v:Discrete mathematics Ročník 345; číslo 12; s. 113169
Hlavní autoři: Bernard, Pierre-Antoine, Crampé, Nicolas, Vinet, Luc
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier 01.12.2022
Témata:
Combinatorics
Mathematics
Dual polar graphs
Terwilliger algebra
quantum groups
ISSN:0012-365X
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Shrnutí: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.
ISSN:0012-365X
DOI:10.1016/j.disc.2022.113169