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The cohomology of real De Concini-Procesi models of Coxeter type. (English) Zbl 1153.14011
The aim of the paper is to study the rational cohomology groups of the real De Concini-Procesi model corresponding to a finite Coxeter group. This is a generalization of the type A case of the moduli space of stable genus zero curves with marked points. The formulae for the Betti numbers in types B and D are given, and exact values of the Betti numbers in exceptional types are computed. The authors also find a generating function for the characters of the representations of a Coxeter group of type B on the rational cohomology groups of the corresponding De Concini-Procesi model, and deduce the multiplicities of one-dimensional characters in the representations, and a formula for the Euler character. A moduli space interpretation of this type B variety is obtained: it is embedded as a closed subvariety in $\overline{{ℳ}_{0,2n+2}}$.
MSC:
 14D20 Algebraic moduli problems, moduli of vector bundles 14N20 Configurations and arrangements of linear subspaces 20F55 Reflection groups; Coxeter groups