Coxeter group actions on the complement of hyperplanes and special involutions

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We consider both standard and twisted action of a (real) Coxeter group G on the complement M_G to the complexified reflection hyperplanes by combining the reflections with complex conjugation. We introduce a natural geometric class of special involutions in G and give explicit formulae which describe both actions on the total cohomology H(M_G,C) in terms of these involutions. As a corollary we prove that the corresponding twisted representation is regular only for the symmetric group S_n, the Weyl groups of type D_{2m+1}, E_6 and dihedral groups I_2 (2k+1) and that the standard action has no anti-invariants. We discuss also the relations with the cohomology of generalised braid groups.
11 pages

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Representation Theory, Group Theory, Geometric Topology, 20F55 (Primary) 52C35, 20F36 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/146788

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0311190
 http://arxiv.org/abs/math/0311190
 J. Eur. Math. Soc. (JEMS) 7 (2005), no. 1, 101--116

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arXiv