Induced Characters of Type D Weyl Groups and the Littlewood-Richardson Rule

TL;DR

This paper provides an explicit decomposition of induced characters from certain subgroups of type D Weyl groups using Littlewood-Richardson coefficients, enhancing understanding of their representation theory.

Contribution

It introduces a new explicit formula for decomposing induced characters of type D Weyl groups in terms of Littlewood-Richardson coefficients.

Findings

Explicit decomposition formulas for induced characters

Connection between Weyl group characters and Littlewood-Richardson coefficients

Enhanced tools for studying type D Weyl group representations

Abstract

For any ordinary irreducible character of a maximal reflection subgroup of type $D_aD_b$ of a type $D$ Weyl group we give an explicit decomposition of the induced character in terms of Littlewood-Richardson coefficients.