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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 1, Pages 96–108 (Mi zvmmf11018)  

Computation of irreducible decompositions of permutation representations of wreath products of finite groups

V. V. Kornyak

Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia

Abstract: An algorithm for the computation of the complete set of primitive orthogonal idempotents of the centralizer ring of the permutation representation of the wreath product of finite groups is described. This set determines the decomposition of the representation into irreducible components. In the quantum mechanics formalism, the primitive idempotents are projection operators onto irreducible invariant subspaces of the Hilbert space describing the states of many-particle quantum systems. The proposed algorithm uses methods of computer algebra and computational group theory. The C implementation of this algorithm is able to construct decompositions of representations of high dimensions and ranks into irreducible components.

Key words: wreath product of groups, permutation representation, centralizer ring, primitive idempotents, decomposition into irreducible subrepresentations, computational group theory.

DOI: https://doi.org/10.31857/S0044466920010123


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:1, 90–101

Bibliographic databases:

UDC: 512.547.2:530.145.81
Received: 24.07.2019
Revised: 24.07.2019
Accepted:18.09.2019

Citation: V. V. Kornyak, “Computation of irreducible decompositions of permutation representations of wreath products of finite groups”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 96–108; Comput. Math. Math. Phys., 60:1 (2020), 90–101

Citation in format AMSBIB
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\pages 96--108
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