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2015 Mackey's criterion for subgroup restriction of Kronecker products and harmonic analysis on Clifford groups
Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli
Tohoku Math. J. (2) 67(4): 553-571 (2015). DOI: 10.2748/tmj/1450798073

Abstract

We present a criterion for multiplicity-freeness of the decomposition of the restriction ${\rm Res}^G_H(\rho_1 \otimes \rho_2)$ of the Kronecker product of two generic irreducible representations $\rho_1, \rho_2$ of a finite group $G$ with respect to a subgroup $H \leq G$. This constitutes a generalization of a well-known criterion due to Mackey (which corresponds to the case $H = G$). The corresponding harmonic analysis is illustated by detailed computations on the Clifford groups $G=\mathbb{CL}(n)$, together with the subgroups $H=\mathbb{CL}(n-1)$, for $n \geq 1$, which lead to an explicit decomposition of the restriction of Kronecker products.

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Tullio Ceccherini-Silberstein. Fabio Scarabotti. Filippo Tolli. "Mackey's criterion for subgroup restriction of Kronecker products and harmonic analysis on Clifford groups." Tohoku Math. J. (2) 67 (4) 553 - 571, 2015. https://doi.org/10.2748/tmj/1450798073

Information

Published: 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1345.20012
MathSciNet: MR3436542
Digital Object Identifier: 10.2748/tmj/1450798073

Subjects:
Primary: 20C15
Secondary: 20G40, 43A90

Rights: Copyright © 2015 Tohoku University

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Vol.67 • No. 4 • 2015
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