The Equivariant Euler Characteristic of Real Coxeter Toric Varieties
نویسنده
چکیده
Let W be a crystallographic Weyl group, and let TW 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 TW (R) is a smooth, connected, compact manifold with a W -action. We give a formula for the Euler characteristic of TW (R) as a generalised character of W . In type An−1 for n odd, one obtains a generalised character of Sym n whose degree is (up to sign) the n Euler number.
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