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 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

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 
@article{JEMS_2005_7_1_a4,
     author = {Giovanni Felder and Alexander P. Veselov},
     title = {Coxeter group actions on the complement of hyperplanes and special involutions},
     journal = {Journal of the European Mathematical Society},
     pages = {101--116},
     year = {2005},
     volume = {7},
     number = {1},
     doi = {10.4171/jems/23},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/23/}
}
TY  - JOUR
AU  - Giovanni Felder
AU  - Alexander P. Veselov
TI  - Coxeter group actions on the complement of hyperplanes and special involutions
JO  - Journal of the European Mathematical Society
PY  - 2005
SP  - 101
EP  - 116
VL  - 7
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/23/
DO  - 10.4171/jems/23
ID  - JEMS_2005_7_1_a4
ER  - 
%0 Journal Article
%A Giovanni Felder
%A Alexander P. Veselov
%T Coxeter group actions on the complement of hyperplanes and special involutions
%J Journal of the European Mathematical Society
%D 2005
%P 101-116
%V 7
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/23/
%R 10.4171/jems/23
%F JEMS_2005_7_1_a4
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

Cité par Sources :