Monday, May 5, 2008
2:30pm - 3:55pm, Science 2-065

Catalin Zara

UMass Boston

Positivity of Equivariant Schubert Classes

Abstract: For a permutation $u$ in $S_n$, the equivariant Schubert class $\mathfrak{S}_u$ is determined by its values at the permutations $v$ that are above $u$ in the Bruhat order. For such $v$, the restriction $\mathfrak{S}_u(v)$ is a polynomial with nonnegative integer coefficients in the simple roots, and a manifestly positive formula for $\mathfrak{S}_u(v)$, as a sum of monomials in positive roots, has been proved by Billey. I will present a new proof of Billey's positive formula (for type A), obtained by applying a degeneration technique to a recent formula of Goldin and Tolman.