Semidirect product decomposition of Coxeter groups

Cédric Bonnafé; Matthew J. Dyer

Semidirect product decomposition of Coxeter groups

Group Theory 2008-07-09 v3

Authors: Cédric Bonnafé , Matthew J. Dyer

Abstract

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.

Keywords

coxeter groups

Cite

@article{arxiv.0805.4100,
  title  = {Semidirect product decomposition of Coxeter groups},
  author = {Cédric Bonnafé and Matthew J. Dyer},
  journal= {arXiv preprint arXiv:0805.4100},
  year   = {2008}
}

Comments

28 pages, one table. We have added some comments on parabolic subgroups, double cosets representatives, finite and affine Weyl groups, invariant theory, Solomon descent algebra

Semidirect product decomposition of Coxeter groups

Abstract

Keywords

Cite

Comments

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