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

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arxiv 2108.13819 v1 pith:HXIKSUMW submitted 2021-08-31 math.CO

Pierre-Antoine Bernard , Nicolas Crampe , Luc Vinet This is my paper · ORCID
classification math.CO
keywords dualpolarsymplecticadjacencyalgebragraphsmatrixsubspace
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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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  1. The Lie algebra $\mathfrak{sl}_4(\mathbb C)$ and the hypercubes

    math.CO 2025-05 conditional novelty 7.0 of 10

    The degree-N polynomials in four variables, the fixed 3-tensors of the hypercube, and the hypercube Terwilliger algebra are all isomorphic as sl4(C)-modules, with explicit maps.

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