# Torus quotient of Richardson varieties in Orthogonal and Symplectic Grassmannians

## TL;DR

This paper establishes criteria for the existence of semistable points in Richardson varieties within orthogonal and symplectic Grassmannians under torus actions, contributing to geometric invariant theory in these contexts.

## Contribution

It provides a new criterion for semistability of Richardson varieties in G/P for groups of types B, C, D, advancing understanding of their geometric invariant theory.

## Key findings

- Criteria for semistability of Richardson varieties established.
- Applicable to groups of types B, C, D.
- Enhances understanding of torus actions on these varieties.

## Abstract

For any simple, simply connected algebraic group $G$ of type $B,C$ and $D$ and for any maximal parabolic subgroup $P$ of $G$, we provide a criterion for a Richardson variety in $G/P$ to admit semistable points for the action of a maximal torus $T$ with respect to an ample line bundle on $G/P$.