(Co)minuscule Schubert Calculus

This talk is based on joint work with Alexander Yong (see math.AG/0608276 and math.CO/0701215). Some of these results and related background were presented in Yong's talk in this seminar on March 9, 2007.

I will discuss a root system uniform, concise combinatorial rule for Schubert calculus of minuscule and cominuscule flag varieties G/P, generalizing Schutzenberger's jeu de taquin formulation of Schubert calculus in type A, and a rule formulated by Worley and Sagan in the Langrangian and orthogonal Grassmannian cases. I will also spend some time discussing the underlying tableau combinatorics of cominuscule dual equivalence, which extends a concept introduced by Haiman. Time permitting, I will discuss a conjecture for K-theory in the minuscule types.