David Hemmer
University of Chicago
Preprint

Abstract:

Kleshchev has recently classified those modules for the symmetric group which have semisimple restriction to any Young subgroup. We determine $\Ext (D^\lambda, D^\mu)$ where $D^\lambda$ and $D^\mu$ are modules of this type, called completely splittable.  As a corollary of this and recent work of Kleshchev and Nakano, we can determine $\Ext_{GL_n(K)}((L(\lambda),L(\mu))$ for certain simple $GL_n(K)-$ modules $L(\lambda)$ and $L(\mu)$.