Gel'fand-Zetlin basis and Clebsch-Gordan coefficients for covariant representations of the Lie superalgebra gl(m)

摘要

A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m). 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) with the natural representation V[1,0,...,0] of gl(m) with highest weight (1,0,...,0) are computed. Both results are steps for the explicit construction of the parastatistics Fock space.