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.
Citation
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
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