# On Certain Tilting Modules for SL2

## TL;DR

This paper characterizes when tensor products of specific modules for SL2 are tilting modules, providing explicit criteria based on p-adic expansions of their highest weights.

## Contribution

It offers a complete, explicit criterion for tilting modules arising from tensor products of induced and Weyl modules for SL2, based on p-adic expansions.

## Key findings

- Complete characterization of tilting tensor products for SL2
- Explicit p-adic expansion criteria for module tilting
- Recursive but explicit conditions for tilting modules

## Abstract

We give a complete picture of when the tensor product of an induced module and a Weyl module is a tilting module for the algebraic group $SL_2$ over an algebraically closed field of characteristic $p$. Whilst the result is recursive by nature, we give an explicit statement in terms of the $p$-adic expansions of the highest weight of each module.