Tuesday, May 14, 15:15, 7.527

Geetha Thangavelu (IISER Thiruvananthapuram), Schur algebras for the alternating group.

Abstract:
The alternating Schur algebra AS_F(n,d) is defined as the commutant of the action of the alternating group A_d on the d-fold tensor power of an n-dimensional F-vector space. We find a basis of AS_F(n,d) in terms of bipartite graphs, and a graphical interpretation of structure constants with respect to this basis. We will also discuss about what additional structure does being a module for the AS_F(n,d) impose on a module for the classical Schur algebra using Koszul duality functor. This is a joint work with Amritanshu Prasad and Shraddha Srivastava.