Chapter

Reduction of SU(n) tensors

Adam M. Bincer

in Lie Groups and Lie Algebras

Published in print October 2012 | ISBN: 9780199662920
Published online January 2013 | e-ISBN: 9780191745492 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199662920.003.0015
Reduction of SU(n) tensors

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Reduction of SU(n) tensors is described. Conjugate representations are identified. The dimension of the totally symmetric and totally antisymmetric tensors is obtained. All irreducible SU(n) tensors of rank r are described in detail for r equal to 2, 3 and 4. These results are specialized for n equal to 2 and 3. The most general irreducible representation of SU(n) corresponding to the partition (f 1, f 2, …, fn) can be specified by the n–1 integers pk = fkfk +1, 1 ≤ kn–1, and a formula is given for its dimension. The reduction of the Kronecker product of two irreducible representations of SU(n) is described. Biographical notes on Kronecker are given.

Keywords: irreducible tensors; dimension of irreducible tensors; conjugate representations; reduction of the Kronecker product

Chapter.  3246 words. 

Subjects: Mathematical and Statistical Physics

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