UC Riverside

In this paper, we study tensor products of Demazure modules for the current algebra $\lie{sl}_2[t]$. We establish a set of generators and relations for the tensor product of two local Weyl modules (which are also level 1 Demazure modules). We also establish a character formula for the tensor product of a level 2 Demazure module and a local Weyl module. To complete the proof of this character formula we also prove a short exact sequence of $V(\xi)$ modules. We further conjecture a character formula for the tensor product of any level $\ell$ Demazure module and a local Weyl module and provide a proof assuming the analogous short exact sequence holds.