Title: Projected Richardson Varieties
Speaker: David Speyer
Speaker Info: Michigan
While the projections of Schubert varieties in a full generalized flag manifold G/B to a partial flag manifold G/P are again Schubert varieties, the projections of Richardson varieties (intersections of Schubert varieties with opposite Schubert varieties) are not always Richardson varieties. The stratification of G/P by projections of Richardson varieties arises in the theory of total positivity and also from Poisson and noncommutative geometry. We show that the projected Richardsons are the only compatibly split subvarieties of G/P (for the standard splitting). In the minuscule case, we describe Groebner degenerations of projected Richardsons. The theory is especially elegant in the case of the Grassmannian, where we obtain the "positroid" varieties, whose combinatorics can be described in terms of juggling patterns.Date: Thursday, May 5, 2011
Joint work with Allen Knutson and Thomas Lam.