Branching properties for the groups G(de,e,r)

TL;DR

This paper investigates how the representations of certain finite complex reflection groups behave when restricted to their maximal parabolic subgroups, focusing on the multiplicity of components and combinatorial symmetry changes.

Contribution

It provides new insights into the restriction of representations of G(de,e,r+1) to G(de,e,r), highlighting combinatorial and symmetry aspects.

Findings

Analysis of multiplicity of components in restrictions

Characterization of symmetry changes in combinatorial necklaces

New results on properties of G(de,e,r) groups

Abstract

We study general properties of the restriction of the representations of the finite complex reflection groups $G(de,e,r+1)$ to their maximal parabolic subgroups of type $G(de,e,r)$, and focus notably on the multiplicity of components. In combinatorial terms, this amounts to the following question : which symmetries arise or disappear when one changes (exactly) one pearl in a combinatorial necklace ?