Seminar on Combinatorics
主講者: 黃皓文 (國立交通大學)
講題: A combinatorial representation of Coxeter groups over a field of two elements
時間: 2008-03-19 (Wed.)  15:00 - 16:00
Abstract: Let W denote a simply-laced Coxeter group with n generators. We construct an n-dimensional representation $\phi$ of W over the finite field $F_2$ of two elements. The action of $\phi(W)$ 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 $\phi(W)$, and conclude that the kernel of $\phi$ is the center Z(W) of W.
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