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arXiv · 0806.0680

The equivariant Euler characteristic of real Coxeter toric varieties

Anthony Henderson·Gus Lehrer
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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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BibTeXRIS

Anthony Henderson, Gus Lehrer. 2008-10-21. The equivariant Euler characteristic of real Coxeter toric varieties. https://doi.org/10.1112/blms%2Fbdp023

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