We present a criterion for multiplicity-freeness of the decomposition of the restriction ResG H(1 ⊗ 2) of the Kronecker product of two generic irreducible represen- tations 1, 2 of a finite group G with respect to a subgroup H ≤ 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 = CL(n), together with the subgroups H = CL(n − 1), for n ≥ 1, which lead to an explicit decomposition of the restriction of Kronecker products.

Ceccherini Silberstein, T., Scarabotti, F., Tolli, F. (2015). Mackey's criterion for subgroup restriction of Kronecker products and harmonic analysis on Clifford groups. TOHOKU MATHEMATICAL JOURNAL, 67(4), 553-571.

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

TOLLI, FILIPPO
2015-01-01

Abstract

We present a criterion for multiplicity-freeness of the decomposition of the restriction ResG H(1 ⊗ 2) of the Kronecker product of two generic irreducible represen- tations 1, 2 of a finite group G with respect to a subgroup H ≤ 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 = CL(n), together with the subgroups H = CL(n − 1), for n ≥ 1, which lead to an explicit decomposition of the restriction of Kronecker products.
2015
Ceccherini Silberstein, T., Scarabotti, F., Tolli, F. (2015). Mackey's criterion for subgroup restriction of Kronecker products and harmonic analysis on Clifford groups. TOHOKU MATHEMATICAL JOURNAL, 67(4), 553-571.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/300286
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