We present a criterion for multiplicity-freeness of the decomposition of the77restriction ResGH(ρ1⊗ρ2)of the Kronecker product of two generic irreducible representations88ρ1,ρ2of a finite groupGwith respect to a subgroupH≤G. This constitutes a generaliza-99tion of a well known criterion due to Mackey (which corresponds to the caseH=G). The1010corresponding harmonic analysis is illustatedby detailed computations on the Clifford groups1111G=CL(n), together with the subgroupsH=CL(n−1),forn≥1, which lead to an explicit1212decomposition of the restriction of Kronecker products
Running electric field gratings for detection of coherent radiation / Montemezzani, Germano; Alonzo, Massimo; Coda, Virginie; Jazbinsek, Mojca; Günter, Peter. - In: JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. B, OPTICAL PHYSICS. - ISSN 0740-3224. - ELETTRONICO. - 32:6(2015), pp. 1078-1083. [10.1364/JOSAB.32.001078]
Running electric field gratings for detection of coherent radiation
ALONZO, Massimo;
2015
Abstract
We present a criterion for multiplicity-freeness of the decomposition of the77restriction ResGH(ρ1⊗ρ2)of the Kronecker product of two generic irreducible representations88ρ1,ρ2of a finite groupGwith respect to a subgroupH≤G. This constitutes a generaliza-99tion of a well known criterion due to Mackey (which corresponds to the caseH=G). The1010corresponding harmonic analysis is illustatedby detailed computations on the Clifford groups1111G=CL(n), together with the subgroupsH=CL(n−1),forn≥1, which lead to an explicit1212decomposition of the restriction of Kronecker products| File | Dimensione | Formato | |
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