Spherical affine cones in exceptional cases and related branching rules

Details Spherical affine cones in exceptional cases and related branching rules Spherical affine cones in exceptional cases and related branching rules

2011-11-16

arxiv.org/abs/1111.3823v1

Mathematics

Representation Theory

Scientific paper

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 $\text{res}^G_H (V^*_{k\omega_i})$, $k \in \N$, 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.

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