Coxeter group actions on the complement of hyperplanes and special involutions
| dc.creator | Felder, Giovanni | |
| dc.creator | Veselov, Alexander P. | |
| dc.date | 2003-11-12 | |
| dc.date | 2004-02-06 | |
| dc.date.accessioned | 2026-07-07T08:56:56Z | |
| dc.date.available | 2026-07-07T08:56:56Z | |
| dc.description | 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. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311190 | |
| dc.identifier | http://arxiv.org/abs/math/0311190 | |
| dc.identifier | J. Eur. Math. Soc. (JEMS) 7 (2005), no. 1, 101--116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146788 | |
| dc.subject | Representation Theory | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F55 (Primary) 52C35, 20F36 (Secondary) | |
| dc.title | Coxeter group actions on the complement of hyperplanes and special involutions | |
| dc.type | text |