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

Anthony Henderson·Eric Rains
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Abstract

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.

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Anthony Henderson, Eric Rains. 2007-07-17. The cohomology of real De Concini-Procesi models of Coxeter type. https://doi.org/10.1093/imrn%2Frnn001

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