Decompositions of the tensor products of irreducible sl(2)-modules in characteristic 3

TL;DR

This paper fully characterizes how tensor products of irreducible sl(2)-modules decompose into indecomposables in characteristic 3, revealing similarities with decompositions in the Lie superalgebra sl(1|1).

Contribution

It provides a complete description of tensor product decompositions for irreducible sl(2)-modules in characteristic 3, a case previously not fully understood.

Findings

Decomposition rules for tensor products in characteristic 3

Resemblance to Lie superalgebra sl(1|1) decompositions

Complete classification of indecomposable modules in this setting

Abstract

We completely describe the decompositions (into indecomposable submodules) of the tensor products of irreducible sl(2)-modules in characteristic 3. The answer resembles analogous decompositions for the Lie superalgebra sl(1|1).