Spherical affine cones in exceptional cases and related branching rules

Abstract

Given a complex simply connected simple algebraic group $G$ of exceptional type and a maximal parabolic subgroup $P\subset G$, we classify all triples $(G,P,H)$ such that $H\subset G$ is a maximal reductive subgroup acting spherically on $G/P$. In addition we derive branching rules for ${\text{res}}_H^G(V_{k{\omega }_i}^{\ast })$, $k\in \mathbb{N}$, where ${\omega }_i$ is the fundamental weight associated to $P$. This is the first of two parts of a project to classify all such triples and corresponding branching rules for all simply connected simple algebraic groups.

References in corpus (1)

• Zhu's algebra and the $C_2$-algebra in the symplectic and the orthogonal cases

Cited by in corpus (2)

• Discrete branching laws for minimal holomorphic representations
• Spherical actions on isotropic flag varieties and related branching rules