The decomposition of the tensor product of representations of the symmetric group
- 1 August 1977
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 18 (8), 1678-1696
- https://doi.org/10.1063/1.523469
Abstract
The decomposition of the tensor product of two irreducible representations of the symmetric group is studied, providing a foundation for the calculation of the Clebsch–Gordon coefficients. Realizations on spaces of polynomials are emphasized. This leads to tensor coupling coefficients. An iterative formula for the calculation of the tensor coupling coefficients is derived, and symmetry constructions are discussed and shown to lead to a reduction in the calculation needed. A well‐defined procedure for the construction of the Clebsch–Gordan coefficients from the tensor coupling coefficients, which works for any multiplicity, is obtained. It may be used for any finite group and, with some modifications, for any compact group.Keywords
This publication has 3 references indexed in Scilit:
- Clebsch–Gordan coefficients of magnetic space groupsJournal of Mathematical Physics, 1976
- Clebsch−Gordan coefficients for *X ⊗ *X in diamond O7h−Fd3m and rocksalt O5n−Fm3mJournal of Mathematical Physics, 1975
- Clebsch−Gordan coefficients for crystal space groupsJournal of Mathematical Physics, 1975