Deligne's category Rep(GL_\delta) and representations of general linear supergroups

TL;DR

This paper classifies indecomposable summands of mixed tensor powers in the representation theory of general linear supergroups, providing formulas for characters and methods for tensor product decomposition.

Contribution

It introduces a classification of indecomposable objects in Deligne's category Rep(GL_ extdelta) and offers new formulas and methods for their tensor product decompositions.

Findings

Classification of indecomposable summands up to isomorphism

Explicit character formulas using supersymmetric Schur polynomials

A new method for decomposing tensor products

Abstract

We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric Schur polynomials, and give a method for decomposing their tensor products. Along the way, we describe indecomposable objects in Rep(GL_\delta) and explain how to decompose their tensor products.