Combinatorial representations of Coxeter groups over a field of two elements

2008/04/14 by Hau-wen Huang, Huang, Hau-wen, Chih-wen Weng +1
Mathematics · #05E18 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05E18

paper · pdf · doi:10.48550/arxiv.0804.2150

20 pages, 2 figures, 2 tables

arxiv created 2010/08/01 · arxiv updated 2010/08/03

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 F₂ of two elements. The action of ϕ(W) on F₂ⁿ 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 F₂ⁿ under the action of ϕ(W), and find that the kernel of ϕ is the center Z(W) of W.

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