Equivariant sheaves on some spherical varieties

TL;DR

This paper characterizes categories of equivariant vector bundles on specific spherical varieties using linear algebra structures like filtrations and group actions.

Contribution

It provides a linear algebraic description of equivariant vector bundles on toroidal spherical varieties, connecting geometric objects to algebraic data.

Findings

Categories described via vector spaces with filtrations and actions

Explicit linear algebraic models for equivariant bundles

Framework applicable to certain toroidal spherical varieties

Abstract

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.