Representation theory of sl(2|1)

TL;DR

This paper provides a comprehensive analysis of finite-dimensional representations of the Lie superalgebra sl(2|1), including tensor product decompositions, by leveraging its relation to gl(1|1) representation theory.

Contribution

It offers a complete classification of finite-dimensional sl(2|1) representations and details tensor product decompositions, advancing understanding of superalgebra representations.

Findings

Complete classification of finite-dimensional sl(2|1) representations

Explicit tensor product decompositions

Relation to gl(1|1) representation theory

Abstract

In this note we present a complete analysis of finite dimensional representations of the Lie superalgebra sl(2|1). This includes, in particular, the decomposition of all tensor products into their indecomposable building blocks. Our derivation makes use of a close relation with the representation theory of gl(1|1) for which analogous results are described and derived.