Geodesic
Coxeter group actions on the complement of hyperplanes and special involutions
Journal of the European Mathematical Society, Tome 7 (2005) no. 1, pp. 101-116.

Voir la notice de l'article provenant de la source EMS Press

We consider both standard and twisted action of a (real) Coxeter group G on the complement MG​ 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∗(MG​,C) in terms of these involutions. As a corollary we prove that the corresponding twisted representation is regular only for the symmetric group Sn​, the Weyl groups of type D2m+1​, E6​ and dihedral groups I2​(2k+1). We discuss also the relations with the cohomology of Brieskorn's braid groups.
DOI : 10.4171/jems/23
Classification : 22-XX, 00-XX
Keywords: Coxeter groups, hyperplane arrangements, Brieskorn's braid groups 
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     title = {Coxeter group actions on the complement of hyperplanes and special involutions},
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Giovanni Felder; Alexander P. Veselov. Coxeter group actions on the complement of hyperplanes and special involutions. Journal of the European Mathematical Society, Tome 7 (2005) no. 1, pp. 101-116. doi : 10.4171/jems/23. http://geodesic.mathdoc.fr/articles/10.4171/jems/23/

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