An algorithm for constructing irreducible decompositions of permutation representations of wreath products of finite groups. (English. Russian original) Zbl 1451.81269
J. Math. Sci., New York 251, No. 3, 375-394 (2020); translation from Zap. Nauchn. Semin. POMI 485, 107-139 (2019).
Summary: 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.
MSC:
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 20C35 | Applications of group representations to physics and other areas of science |
| 20B05 | General theory for finite permutation groups |
| 20E22 | Extensions, wreath products, and other compositions of groups |
| 47A15 | Invariant subspaces of linear operators |
| 81V72 | Particle exchange symmetries in quantum theory (general) |
| 81-08 | Computational methods for problems pertaining to quantum theory |
| 20-08 | Computational methods for problems pertaining to group theory |
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