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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 468, Pages 228–248
(Mi znsl6587)
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This article is cited in 2 scientific papers (total in 2 papers)
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An algorithm for decomposition of finite group representations by means of invariant projectors
V. V. Kornyak Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia
Abstract:
We describe an algorithm for decomposition of permutation representations of finite groups over fields of characteristic zero into irreducible components.
The algorithm is based on the fact that the components of the invariant inner product in invariant subspaces are operators of projection into these subspaces. This allows us to reduce the problem to solving systems of quadratic equations. The current implementation of the proposed algorithm allows us to split representationы of dimensions up to hundreds of thousands. Computational examples are given.
Key words and phrases:
finite group, permutation representation, irreducible representation, invariant bilinear form, computational group theory.
Received: 10.09.2018
Citation:
V. V. Kornyak, “An algorithm for decomposition of finite group representations by means of invariant projectors”, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Zap. Nauchn. Sem. POMI, 468, POMI, St. Petersburg, 2018, 228–248; J. Math. Sci. (N. Y.), 240:5 (2019), 651–664
Linking options:
https://www.mathnet.ru/eng/znsl6587 https://www.mathnet.ru/eng/znsl/v468/p228
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Abstract page: | 113 | Full-text PDF : | 33 | References: | 15 |
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