Generalized Young Tableaux and the General Linear Group
- 1 January 1970
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (1) , 280-293
- https://doi.org/10.1063/1.1665059
Abstract
A generalization of the Young tableau is defined, and use is made of this in the study of some of the properties of the irreducible representations (IR's) of each of the linear groups in n dimensions induced in a space defined by mixed tensors without recourse to lowering or raising of indices. A formula for the dimensions of any IR of Ln is given. Procedures are derived for the reduction of the outer product of such IR's and for the decomposition of these IR's into IR's of some subgroups of interest in the theory of elementary particles.Keywords
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