Branching rules for the Weyl Groups of the Unitary and Orthogonal Lie Groups

TL;DR

This paper introduces a method to compute how characters of symmetric groups decompose when restricted to hyperoctahedral groups, aiding representation analysis of these algebraic structures.

Contribution

It provides a new procedure for reducing characters of symmetric groups in terms of hyperoctahedral group characters, enhancing understanding of their representation relationships.

Findings

Established a systematic reduction procedure

Connected symmetric and hyperoctahedral group characters

Facilitated calculations of induced and irreducible characters

Abstract

This note presents a procedure to determine the reduction of the irreducible and the induced characters of the symmetric group in terms of the irreducible and induced characters of the hyperoctahedral group Key Words: Symmetric Group, Hyperoctahedral group, Representations, Characters, Re- duction.