Projected Richardson varieties and affine Schubert varieties

Details Projected Richardson varieties and affine Schubert varieties Projected Richardson varieties and affine Schubert varieties

2011-06-14

arxiv.org/abs/1106.2586v2

Mathematics

Algebraic Geometry

20 pages. A new section on K-theory comparison is added

Scientific paper

Let $G$ be a complex simple algebraic group and $G/P$ be a partial flag variety. The projections of Richardson varieties from the full flag variety form a stratification of $G/P$. We show that the closure partial order of projected Richardson varieties agrees with that of a subset of Schubert varieties in the affine flag variety of $G$. Furthermore, we compare the torus-equivariant cohomology and $K$-theory classes of these two stratifications by pushing or pulling these classes to the affine Grassmannian. Our work generalizes results of Knutson, Lam, and Speyer for the Grassmannian of type $A$.

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