Branching rules for a class of typical and atypical representations of gl(m‖n)

Abstract

The irreducible representations of the Lie superalgebra gl(m‖n) with highest weights of the form Λ=(λ1,λ2,...λm‖ω̇) are investigated using a recently introduced induced module construction for atypical modules. The gl(m‖n)↓gl(m‖n−1) branching rules are obtained and a suitable Gel’fand–Tsetlin basis is introduced. The class of representations considered includes some multiply atypical irreducible representations of gl(m‖n) and all irreducible representations of gl(m‖1).