2010-09-10

Allen Knutson

Frobenius splitting of flag manifolds and projected Richardson varieties

Although Schubert varieties in full flag manifolds G/B project again to Schubert varieties in partial flag manifolds G/P, the same is not always true of Schubert intersect opposite Schubert, known as Richardson varieties. It turns out that a single stratification of G/P, into its projected Richardson varieties, is the most natural from the point of view of nonnegative real, characteristic p, Poisson, and noncommutative geometry. I will define "Frobenius splittings" and explain the fact that the "compatibly split" subvarieties of G/P are exactly the projected Richardson varieties. This work is joint with Thomas Lam and David Speyer.