Advanced Search

We consider both standard and twisted actions 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...