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Published February 14, 2008 | Submitted
Journal Article Open

The cohomology of real De Concini–Procesi models of Coxeter type


We study the rational cohomology groups of the real De Concini–Procesi model corresponding to a finite Coxeter group, generalizing the type-A case of the moduli space of stable genus 0 curves with marked points. We compute the Betti numbers in the exceptional types, and give formulae for them in types B and D. We give a generating-function formula for the characters of the representations of a Coxeter group of type B on the rational cohomology groups of the corresponding real De Concini–Procesi model, and deduce the multiplicities of one-dimensional characters in the representations, and a formula for the Euler character. We also give a moduli space interpretation of this type-B variety, and hence show that the action of the Coxeter group extends to a slightly larger group.

Additional Information

© The Author 2008. Received July 19, 2007; Revised July 19, 2007; Accepted January 4, 2008. This work was supported by Australian Research Council grant DP0344185

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