The saturation property for branching rules -- Examples

TL;DR

This paper investigates the decomposition of irreducible modules for certain pairs of reductive groups, demonstrating the saturation property across all examined examples, which enhances understanding of branching rules in representation theory.

Contribution

It provides the first systematic study of the saturation property for specific pairs of reductive groups in the context of branching rules.

Findings

Saturation property holds for all examined group pairs

Examples include specific reductive group pairs

Insights into the structure of module decompositions

Abstract

For a few pairs $G\subset \hat G$ of reductive groups, we study the decomposition of irreducible $\hait G$-modules into $G$-modules. In particular, we observe the saturation property for all of these pairs.