Rational cohomology of the real Coxeter toric variety of type A

Details Rational cohomology of the real Coxeter toric variety of type A Rational cohomology of the real Coxeter toric variety of type A

2010-11-17

arxiv.org/abs/1011.3860v1

Mathematics

Representation Theory

10 pages

Scientific paper

The toric variety corresponding to the Coxeter fan of type A can also be described as a De Concini-Procesi wonderful model. Using a general result of Rains which relates cohomology of real De Concini-Procesi models to poset homology, we give formulas for the Betti numbers of the real toric variety, and the symmetric group representations on the rational cohomologies. We also show that the rational cohomology ring is not generated in degree 1.

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