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Coxeter group actions on the complement of hyperplanes and special involutions | | Giovanni Felder
; Alexander P. Veselov
; | | Date: |
12 Nov 2003 | | Subject: | Representation Theory; Group Theory; Geometric Topology MSC-class: 20F55 (Primary) 52C35, 20F36 (Secondary) | math.RT math.GR math.GT | | Affiliation: | ETH Zurich) and Alexander P. Veselov (Loughborough University and Landau Institute | | Abstract: | 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. | | Source: | arXiv, math.RT/0311190 | | Services: | Forum | Review | PDF | Favorites | |
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