Jacobi–Trudi type formula for a class of irreducible representations of 𝔤𝔩(m|n)

Abstract

We prove a determinantal type formula to compute the characters of a class of finite-dimensional irreducible representations of the general Lie super-algebra [Formula: see text] in terms of the characters of the symmetric powers of the fundamental representation and their duals. This formula, originally conjectured by van der Jeugt and Moens, can be regarded as a generalization of the well-known Jacobi–Trudi formula.