Tensor products of psl(2|2) representations

TL;DR

This paper analyzes finite-dimensional representations of the Lie superalgebra psl(2|2), decomposing tensor products of various types and discovering new indecomposable modules, with potential applications in string theory backgrounds.

Contribution

It provides a comprehensive decomposition of tensor products involving typical and atypical psl(2|2) representations, including the discovery of new indecomposables.

Findings

Tensor products of long multiplets and projective covers close among themselves.

An infinite family of new indecomposables appears in tensor products of two short multiplets.

Remarks on applications to AdS_3 backgrounds in string theory.

Abstract

The aim of this work is to study finite dimensional representations of the Lie superalgebra psl(2|2) and their tensor products. In particular, we shall decompose all tensor products involving typical (long) and atypical (short) representations as well as their so-called projective covers. While tensor products of long multiplets and projective covers close among themselves, we shall find an infinite family of new indecomposables in the tensor products of two short multiplets. Our note concludes with a few remarks on possible applications to the construction of AdS_3 backgrounds in string theory.