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HOME > Table of Contents and Abstracts > Vol. 67, No. 4
Tohoku Mathematical Journal
2015
December
SECOND SERIES VOL. 67, NO. 4
Tohoku Math. J.
67 (2015), 553-571
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Title
MACKEY'S CRITERION FOR SUBGROUP RESTRICTION OF KRONECKER PRODUCTS AND HARMONIC ANALYSIS ON CLIFFORD GROUPS
Author
Tullio Ceccherini-Silberstein, Fabio Scarabotti and Filippo Tolli
(Received January 28, 2014, revised July 30, 2014) |
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.
Mathematics Subject Classification.
Primary 20C15; Secondary 43A90, 20G40.
Key words and phrases.
Representation theory of finite groups, Gelfand pair, Mackey's criterion, Kronecker product, Clifford groups.
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