Schur classified polynomial representations of GL(n) using the commuting actions of the dth symmetric group and GL(n) on the d-fold tensor power of n-dimensional space. We set out to investigate what happens when the symmetric group in this picture is shrunk to the alternating group. This led to a simple interpretation and clearer understanding of the Koszul duality functor on the category of polynomial representations of GL(n).

This is based on joint work with T. Geetha and Shraddha Srivastava (https://arxiv.org/abs/1902.02465).