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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Bibliographic Details
Published in:Discrete mathematics Vol. 345; no. 12; p. 113169
Main Authors: Bernard, Pierre-Antoine, Crampé, Nicolas, Vinet, Luc
Format: Journal Article
Language:English
Published: Elsevier 01.12.2022
Subjects:
Combinatorics
Mathematics
Dual polar graphs
Terwilliger algebra
quantum groups
ISSN:0012-365X
Online Access:Get full text
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Summary: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