Unitary branching rules for the general linear Lie superalgebra

TL;DR

This paper establishes branching rules for finite dimensional unitary modules of the general linear Lie superalgebra using Howe duality and Kac modules, including dual modules of type 2.

Contribution

It introduces new branching rules for unitary modules of rak{gl}_{m|n} and extends to dual type 2 modules, advancing understanding of their structure.

Findings

Derived branching rules for unitary modules using Howe duality.

Established dual branching rules for type 2 unitary modules.

Enhanced the classification of finite dimensional modules of rak{gl}_{m|n}.

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.