The equivariant Euler characteristic of real Coxeter toric varieties

Details The equivariant Euler characteristic of real Coxeter toric varieties The equivariant Euler characteristic of real Coxeter toric varieties

Publishing date

2008-06-04

URL

arxiv.org/abs/0806.0680v2

Journals

Bull. London Math. Soc. 41 (2009), no. 3, pp. 515-523

Science

Mathematics

Field

Representation Theory

Additional info

10 pages. Version 2 incorporates slight revisions made at the suggestion of the referee

Type

Scientific paper

Digital Object Identifier

10.1112/blms/bdp023

Abstract

Let $W$ be a Weyl group, and let $\CT_W$ be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of $W$, and its weight lattice. The real locus $\CT_W(\R)$ is a smooth, connected, compact manifold with a $W$-action. We give a formula for the equivariant Euler characteristic of $\CT_W(\R)$ as a generalised character of $W$. In type $A_{n-1}$ for $n$ odd, one obtains a generalised character of $\Sym_n$ whose degree is (up to sign) the $n^{\text{th}}$ Euler number.

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