Super tableaux and a branching rule for the general linear Lie superalgebra

TL;DR

This paper develops branching rules for simple polynomial modules of the Lie superalgebra gl(m|n), using generalized tableaux and Borel subalgebra conjugacy classes, providing a combinatorial basis for these modules.

Contribution

It introduces a new formulation of branching rules for gl(m|n) modules based on Borel subalgebra conjugacy classes and constructs Gelfand-Tsetlin bases using generalized tableaux.

Findings

Branching rules depend on Borel subalgebra conjugacy classes

Gelfand-Tsetlin bases constructed via generalized semistandard tableaux

Provides a combinatorial framework for polynomial modules of gl(m|n)

Abstract

In this note, we formulate and prove branching rules of simple polynomial modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. Our branching rules depend on the conjugacy class of the Borel subalgebra. A Gelfand-Tsetlin basis of a polynomial module associated to each Borel subalgebra is obtained in terms of generalized semistandard tableaux.