Tohoku Mathematical Journal

Mackey's criterion for subgroup restriction of Kronecker products and harmonic analysis on Clifford groups

Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli

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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.

Article information

Source
Tohoku Math. J. (2), Volume 67, Number 4 (2015), 553-571.

Dates
First available in Project Euclid: 22 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1450798073

Digital Object Identifier
doi:10.2748/tmj/1450798073

Mathematical Reviews number (MathSciNet)
MR3436542

Zentralblatt MATH identifier
1345.20012

Subjects
Primary: 20C15: Ordinary representations and characters
Secondary: 43A90: Spherical functions [See also 22E45, 22E46, 33C55] 20G40: Linear algebraic groups over finite fields

Keywords
Representation theory of finite groups Gelfand pair Mackey's criterion Kronecker product Clifford groups

Citation

Ceccherini-Silberstein, Tullio; Scarabotti, Fabio; Tolli, Filippo. Mackey's criterion for subgroup restriction of Kronecker products and harmonic analysis on Clifford groups. Tohoku Math. J. (2) 67 (2015), no. 4, 553--571. doi:10.2748/tmj/1450798073. https://projecteuclid.org/euclid.tmj/1450798073


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References

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