**R. Venkatesh**

TIFR

July 24, 2014

**Tensor product decomposition of $g$--stable Demazure modules**:
Let $g$ be a finite--dimensional simple complex Lie algebra. The
$g$--stable Demazure modules of the untwisted affine Lie algebra associated to $g$ naturally become finite--dimensional graded modules for the current algebra $g[t]$ by restriction. In this talk, I will discuss results on the tensor product structure of these $g[t]$--modules and its connection with several important conjectures.?? This is joint work with Vyjayanthi Chari, Peri Shereen and Jeffrey Wand.