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

TL;DR

This paper develops a Gel'fand-Zetlin basis for covariant tensor representations of the Lie superalgebra gl(m|n), providing explicit generator actions and Clebsch-Gordan coefficients, advancing the construction of the parastatistics Fock space.

Contribution

It introduces a Gel'fand-Zetlin basis for covariant representations of gl(m|n) and computes Clebsch-Gordan coefficients for tensor products, enabling explicit construction of the parastatistics Fock space.

Findings

Explicit Gel'fand-Zetlin basis for covariant representations

Derived generator actions on the basis

Computed Clebsch-Gordan coefficients for tensor products

Abstract

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.