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

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.