# Spherical actions on isotropic flag varieties and related branching rules

## TL;DR

This paper classifies spherical actions of subgroups on flag varieties of symplectic and orthogonal groups and determines the restriction rules for irreducible representations in these settings.

## Contribution

It provides a complete classification of triples (G,H,X) with spherical H-actions on flag varieties and explicitly describes the restriction of G-representations to H.

## Key findings

- Classification of all spherical triples (G,H,X) for symplectic and orthogonal groups.
- Explicit restriction rules for irreducible representations from G to H.
- Identification of cases with spherical subgroup actions on flag varieties.

## Abstract

Let $G$ be a symplectic or special orthogonal group, let $H$ be a connected reductive subgroup of $G$, and let $X$ be a flag variety of $G$. We classify all triples $(G,H,X)$ such that the natural action of $H$ on $X$ is spherical. For each of these triples, we determine the restrictions to $H$ of all irreducible representations of $G$ realized in spaces of sections of homogeneous line bundles on $X$.