Coxeter group actions on the complement of hyperplanes and special involutions

Felder, Giovanni, and Veselov, A.. "Coxeter group actions on the complement of hyperplanes and special involutions." Journal of the European Mathematical Society 007.1 (2005): 101-116. <http://eudml.org/doc/277491>.

@article{Felder2005,
abstract = {We consider both standard and twisted actions of a (real) Coxeter group $G$ on the complement $\mathcal \{M\}_G$ 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 $H^*(\mathcal \{M\}_G,\mathcal \{C\})$ 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 $I_2(2k+1)$. We also discuss the relations with the cohomology of Brieskorn’s braid groups.},
author = {Felder, Giovanni, Veselov, A.},
journal = {Journal of the European Mathematical Society},
keywords = {Coxeter groups; hyperplane arrangements; Brieskorn's braid groups; Coxeter groups; hyperplane arrangements; Brieskorn braid groups},
language = {eng},
number = {1},
pages = {101-116},
publisher = {European Mathematical Society Publishing House},
title = {Coxeter group actions on the complement of hyperplanes and special involutions},
url = {http://eudml.org/doc/277491},
volume = {007},
year = {2005},
}

TY - JOUR
AU - Felder, Giovanni
AU - Veselov, A.
TI - Coxeter group actions on the complement of hyperplanes and special involutions
JO - Journal of the European Mathematical Society
PY - 2005
PB - European Mathematical Society Publishing House
VL - 007
IS - 1
SP - 101
EP - 116
AB - We consider both standard and twisted actions of a (real) Coxeter group $G$ on the complement $\mathcal {M}_G$ 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 $H^*(\mathcal {M}_G,\mathcal {C})$ 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 $I_2(2k+1)$. We also discuss the relations with the cohomology of Brieskorn’s braid groups.
LA - eng
KW - Coxeter groups; hyperplane arrangements; Brieskorn's braid groups; Coxeter groups; hyperplane arrangements; Brieskorn braid groups
UR - http://eudml.org/doc/277491
ER -