Standard Young tableaux and weight multiplicities of the classical Lie groups
- 1 October 1983
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 16 (14) , 3153-3177
- https://doi.org/10.1088/0305-4470/16/14/012
Abstract
By examining the branching rules for all irreducible representations of the classical groups U(k), SU(k), SO(2k+1), Sp(2k) and SO(2k) on restriction to U(1)*U(1)*U(1), standard Young tableaux are specified for each of these groups. It is shown that these tableaux determine the corresponding characters of the irreducible representations. The rules for constructing these tableaux are derived and in this way the determination of weight multiplicities is reduced to a simple combinatorial exercise. General formula for such weight multiplicities are given encompassing the most difficult case: namely that of SO(2k). Illustrative examples are provided, including some yielding the explicit k-dependence of weight multiplicities.Keywords
This publication has 18 references indexed in Scilit:
- Kronecker products for compact semisimple Lie groupsJournal of Physics A: General Physics, 1983
- U(1) factors in branching rulesPhysica A: Statistical Mechanics and its Applications, 1982
- Branching rules for classical Lie groups using tensor and spinor methodsJournal of Physics A: General Physics, 1975
- Modification Rules and Products of Irreducible Representations of the Unitary, Orthogonal, and Symplectic GroupsJournal of Mathematical Physics, 1971
- Spin Representations of the Orthogonal GroupsJournal of Mathematical Physics, 1970
- Formation and decay of negative-parity baryon resonances in a brokenU 6,6 modelIl Nuovo Cimento A (1971-1996), 1970
- Construction of Weight Spaces for Irreducible Representations of An, Bn, Cn, DnJournal of Mathematical Physics, 1970
- Generalized Young Tableaux and the General Linear GroupJournal of Mathematical Physics, 1970
- Inner and Restriction Multiplicity for Classical GroupsJournal of Mathematical Physics, 1969
- Branching Theorem for the Symplectic GroupsJournal of Mathematical Physics, 1967