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arXiv · 0804.2150

Combinatorial representations of Coxeter groups over a field of two elements

Hau-wen Huang·Chih-wen Weng
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Abstract

Let $W$ denote a simply-laced Coxeter group with $n$ generators. We construct an $n$-dimensional representation $ϕ$ of $W$ over the finite field $F_2$ of two elements. The action of $ϕ(W)$ on $F_2^n$ by left multiplication is corresponding to a combinatorial structure extracted and generalized from Vogan diagrams. In each case W of types A, D and E, we determine the orbits of $F_2^n$ under the action of $ϕ(W)$, and find that the kernel of $ϕ$ is the center $Z(W)$ of $W.$

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Hau-wen Huang, Chih-wen Weng. 2010-08-01. Combinatorial representations of Coxeter groups over a field of two elements. https://arxiv.org/abs/0804.2150

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