Algebraic expressions for \(\text{O}(N)\supset \text{O}(N-1)\) reduction factors for the three-rowed irreducible representations. (English) Zbl 0910.22022
Explicit algebraic expressions for all \(\text{O}(N)\supset \text{O}(N-1)\) reduction factors (reduced Wigner coefficients) for the three-row irreducible representations are derived by making use of the irreducible tensor basis method (Baird, Biedenharn, 1963, 1964, 1965; Sun, 1965) and by taking into account the properties of the irreducible tensor operator. The basic results on \(\text{O}(3)\) are reviewed. The irreducible tensor basis of \(\text{O}(4)\) is constructed and the reduction factors of \(\text{O}(4)\supset \text{O}(3)\) are evaluated. Finally, the reduction factors of the general case \(\text{O}(N)\supset \text{O}(N-1)\) for the three-row irreducible representations of \(\text{O}(N)\) and \(\text{O}(N-1)\) are constructed and explicitly calculated. The obtained results are summarized in the related extended tables.
Reviewer: A. A. Bogush (Minsk)
MSC:
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 20G20 | Linear algebraic groups over the reals, the complexes, the quaternions |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
Keywords:
orthogonal groups; reduction factors; irreducible representations; irreducible tensor operatorReferences:
| [1] | DOI: 10.1016/0003-4916(79)90347-6 · doi:10.1016/0003-4916(79)90347-6 |
| [2] | DOI: 10.1016/0003-4916(84)90052-6 · doi:10.1016/0003-4916(84)90052-6 |
| [3] | DOI: 10.1088/0305-4470/28/22/017 · Zbl 0877.22009 · doi:10.1088/0305-4470/28/22/017 |
| [4] | DOI: 10.1063/1.1703728 · Zbl 0098.12802 · doi:10.1063/1.1703728 |
| [5] | Ališauskas S. J., Part. Nuclei 14 pp 1336– (1983) |
| [6] | Ališauskas S. J., Sov. J. Part. Nucl. 14 pp 563– (1983) |
| [7] | DOI: 10.1088/0305-4470/20/1/013 · Zbl 0641.22009 · doi:10.1088/0305-4470/20/1/013 |
| [8] | DOI: 10.1063/1.528122 · Zbl 0659.22016 · doi:10.1063/1.528122 |
| [9] | DOI: 10.1063/1.1704732 · Zbl 0162.58302 · doi:10.1063/1.1704732 |
| [10] | DOI: 10.1063/1.1704732 · Zbl 0162.58302 · doi:10.1063/1.1704732 |
| [11] | DOI: 10.1063/1.1704732 · Zbl 0162.58302 · doi:10.1063/1.1704732 |
| [12] | DOI: 10.1007/BF02773434 · doi:10.1007/BF02773434 |
| [13] | DOI: 10.1063/1.526897 · Zbl 0567.22012 · doi:10.1063/1.526897 |
| [14] | DOI: 10.1063/1.527239 · doi:10.1063/1.527239 |
| [15] | DOI: 10.1088/0305-4470/22/10/007 · Zbl 0694.22015 · doi:10.1088/0305-4470/22/10/007 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
