Deligne's category Rep(GL_δ) and representations of general linear supergroups

2011/08/02 by Jonathan Comes, Comes, Jonathan, Benjamin Wilson +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1108.0652

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_δ) and explain how to decompose their tensor products.

Related

• Tensor Representations of the General Linear Supergroup
• Thick Ideals in Deligne's category \underlineRe p(O_δ)
• On supergroups and their semisimplified representation categories
• Representation theory in complex rank, I
• Representation Theory of General Linear Supergroups in Characteristic 2