Spherical functions on spherical varieties

Intersection Theory on Spherical Varieties

Character Sheaves on Certain Spherical Varieties

We study a class of perverse sheaves on some spherical varieties which include the strata of the De Concini-Procesi completion of a symmetric variety. This is a generalization of the theory of (parabolic) character sheaves.

Equivariant sheaves on some spherical varieties

In this announcement we describe categories of equivariant vector bundles on certain “spherical” varieties. Our description is in linear-algebra terms: vector spaces equipped with filtrations, group and Lie-algebra actions, and linear maps preserving these structures. The two parents of our description are i) the description of G-equivariant vector bundles on homogeneous spaces G/H as H-represe...

Uniqueness Properties for Spherical Varieties

The goal of these lectures is to explain speaker’s results on uniqueness properties of spherical varieties. By a uniqueness property we mean the following. Consider some special class of spherical varieties. Define some combinatorial invariants for spherical varieties from this class. The problem is to determine whether this set of invariants specifies a spherical variety in this class uniquely...

Toric Degenerations of Spherical Varieties

We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by Mirror Symmetry, we give conditions for the limit toric variety to be a Gorenstein Fano, and provide many examples. We also provide an explanation for the limits as boundary points of the moduli space of stable pairs whose exist...