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John Vincent Morales (東北大学）「Some algebras related to the nth extension of Z_4-cycle」

In 1992, Terwilliger introduced a tool to study combinatorial objects such as graphs, codes and designs. This tool later became known as Terwilliger algebra. In this presentation we consider two Terwilliger algebras: of the Z_4-cycle with respect to the vertex 0 and of the extension with respect to the vertex (0,...,0). Let these be denoted by T and T', respectively.

Our results are summarized as follows:

i) There exists a Lie algebra homomorphism from sl_3(C) to T. By extension, there exists an algebra homomorphism from U(sl_3(C)) to the nth symmetric tensor Sym(T). Let U denote the homomorphic image of U(sl_3(C)).

ii) The algebra Sym(T) coincides with T'. Hence, U is a subalgebra of T'.

iii) Every irreducible U-module is T'-invariant. Thus, each irreducible U-module is an irreducible T'-module.