Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)

Details Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n) Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)

2010-04-14

arxiv.org/abs/1004.2381v1

Physics

Mathematical Physics

16 pages

Scientific paper

A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie superalgebra acting on this basis are determined. Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl(m|n) with the natural representation V ([1,0,...,0]) of gl(m|n) with highest weight (1,0,. . . ,0) are computed. Both results are steps for the explicit construction of the parastatistics Fock space.

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