Algebra Seminar
Speaker: Letitia Banu (Western)
"Betti numbers of a rationally smooth toric variety"
Time: 12:30
Room: MC 108
Consider an irreducible representation of a semisimple algebraic group with λ its highest weight and look at the action of the Weyl group W on the rational vector space spanned by the roots. Take the convex hull of the W-orbit of λ and obtain the polytope Pλ=Conv(W.λ). We are interested in describing the Betti numbers of the toric variety X(J) associated to the polytope Pλ when the Weyl group is the n symmetric group and X(J) is a rationally smooth variety which doesn't depend on the highest weight λ but on the set of reflections that fix λ called J. The main result is a recursion formula for the Betti numbers of X(J) in terms of Eulerian polynomials. The theory of algebraic monoids developed by Renner and Putcha is effectively used in our computations.