The equivariant Euler characteristic of real Coxeter toric varieties

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 eq...

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Bibliographic Details
Published in:arXiv.org 2008-10
Main Authors: Henderson, Anthony, Lehrer, Gus
Format: Article
Language:English
Subjects:
Cones
Hyperplanes
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0806.0680