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- Title
An Algorithm for Constructing Irreducible Decompositions of Permutation Representations of Wreath Products of Finite Groups.
- Authors
Kornyak, V. V.
- Abstract
We describe an algorithm for decomposing permutation representations of wreath products of finite groups into irreducible components. The algorithm is based on the construction of a complete set of mutually orthogonal projections to irreducible invariant subspaces of the Hilbert space of the representation under consideration. In constructive models of quantum mechanics, the invariant subspaces of representations of wreath products describe the states of multicomponent quantum systems. The suggested algorithm uses methods of computer algebra and computational group theory. The C implementation of the algorithm is capable of constructing irreducible decompositions of representations of wreath products of high dimensions and ranks. Examples of calculations are given. Bibliography: 15 titles.
- Subjects
ALGORITHMS; FINITE groups; GROUP products (Mathematics); GROUP algebras; INVARIANT subspaces; PERMUTATION groups; WREATH products (Group theory)
- Publication
Journal of Mathematical Sciences, 2020, Vol 251, Issue 3, p375
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-020-05098-0