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.