Semidirect product decomposition of Coxeter groups

Details Semidirect product decomposition of Coxeter groups Semidirect product decomposition of Coxeter groups

2008-05-27

arxiv.org/abs/0805.4100v3

Mathematics

Group Theory

28 pages, one table. We have added some comments on parabolic subgroups, double cosets representatives, finite and affine Weyl

Scientific paper

Let $(W,S)$ be a Coxeter system, let $S=I \dot{\cup} J$ be a partition of $S$ such that no element of $I$ is conjugate to an element of $J$, let $\widetilde{J}$ be the set of $W_I$-conjugates of elements of $J$ and let $\widetilde{W}$ be the subgroup of $W$ generated by $\widetilde{J}$. We show that $W=\widetilde{W} \rtimes W_I$ and that $(\widetilde{W},\widetilde{J})$ is a Coxeter system.

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