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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