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arXiv · 2108.13819

The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and $U_q(sl_2)$

Pierre-Antoine Bernard·Nicolas Crampe·Luc Vinet
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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 $U_q(sl_2)$ 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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Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet. 2021-08-31. The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and $U_q(sl_2)$. https://arxiv.org/abs/2108.13819

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