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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn001, 29 pages, doi:10.1093/imrn/rnn001 published on February 14, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

The Cohomology of Real De Concini–Procesi Models of Coxeter Type

Anthony Henderson1 and Eric Rains2

1 School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
2 Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA

Correspondence: Correspondence to be sent to: anthonyh{at}maths.usyd.edu.au

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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This Article
Right arrow Abstract Freely available
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