The equivariant Euler characteristic of real Coxeter toric varieties

Anthony Henderson and Gus Lehrer

Abstract

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 Symn whose degree is (up to sign) the nth Euler number.

Available as pdf (10 pages).

Also available from the Mathematics ArXiv at arXiv:0806.0680 [math.RT].


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