Unitary branching rules for the general linear Lie superalgebra

Abstract

In terms of highest weights, we establish branching rules for finite dimensional unitary simple modules of the general linear Lie superalgebra ${\mathfrak{gl}}_{m|n}$. Our proof uses the Howe duality for ${\mathfrak{gl}}_{m|n}$, as well as branching rules for Kac modules. Moreover, we derive the branching rules of type 2 unitary simple ${\mathfrak{gl}}_{m|n}$-modules, which are dual to the aforementioned unitary modules.

14 pages