Search
Search Results
-
Toroidal Schubert Varieties
Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads...
-
Spherical Tropical Geometry: a Survey of Recent Developments
This is a survey of some recent results on spherical tropical geometry.
-
Branching Rules Related to Spherical Actions on Flag Varieties
Let G be a connected semisimple algebraic group and let H ⊂ G be a connected reductive subgroup. Given a flag variety X of G , a result of Vinberg and...
-
Orbits of Real Semisimple Lie Groups on Real Loci of Complex Symmetric Spaces
Let G be a complex semisimple algebraic group and X be a complex symmetric homogeneous G -variety. Assume that both G , X as well as the G -action on X ...
-
Transition formulas for involution Schubert polynomials
The orbits of the orthogonal and symplectic groups on the flag variety are in bijection, respectively, with the involutions and fixed-point-free...
-
Lectures on Wonderful Varieties
These notes are an introduction to wonderful varieties. We discuss some general results on their geometry, their role in the theory of spherical...
-
The Cox ring of a complexity-one horospherical variety
Cox rings are intrinsic objects naturally generalizing homogeneous coordinate rings of projective spaces. A complexity-one horospherical variety is a...
-
Levi Subgroup Actions on Schubert Varieties, Induced Decompositions of their Coordinate Rings, and Sphericity Consequences
Let L w be the Levi part of the stabilizer Q w in G L N (for left multiplication) of a Schubert variety X ( w ) in the Grassmannian G ...
-
On Some Families of Smooth Affine Spherical Varieties of Full Rank
Let G be a complex connected reductive group. Losev has shown that a smooth affine spherical G -variety X is uniquely determined by its weight monoid,...
-
Embeddings of Spherical Homogeneous Spaces
We review in these notes the theory of equivariant embeddings of spherical homogeneous spaces. Given a spherical homogeneous space G/H , the normal...
-
Localization in equivariant operational K-theory and the Chang–Skjelbred property
We establish a localization theorem of Borel–Atiyah-Segal type for the equivariant operational K -theory of Anderson and Payne (Doc Math 20:357–399,
2015... -
Sanya Lectures: Geometry of Spherical Varieties
These are expanded notes from lectures on the geometry of spherical varieties given in Sanya. We review some aspects of the geometry of spherical...
-
Standard Monomial Theory for Wonderful Varieties
A general setting for a standard monomial theory on a multiset is introduced and applied to the Cox ring of a wonderful variety. This gives a...
-
Equivariant Degenerations of Spherical Modules: Part II
We determine, under a certain assumption, the Alexeev–Brion moduli scheme M of affine spherical G -varieties with a prescribed weight monoid . In...
-
A combinatorial smoothness criterion for spherical varieties
We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces,...
-
Normal Analytic Compactifications of \(\mathbb{C}^{2}\)
This is a survey of some results on the structure and classification of normal analytic compactifications of...
-
Shintani Functions, Real Spherical Manifolds, and Symmetry Breaking Operators
For a pair of reductive groups G ⊃ G′, we prove a geometric criterion for the space Sh(λ, ν) of Shintani functions to be finite-dimensional in the...
-
Compactification of Drinfeld modular varieties and Drinfeld modular forms of arbitrary rank
We give an abstract characterization of the Satake compactification of a general Drinfeld modular variety. We prove that it exists and is unique up...