2.30 pm, Lecture Hall 5
Schur Algebras for the Alternating Group and Koszul Duality
Institute of Mathematical Sciences, Chennai.
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 tensors of an n-dimensional F-vector space. It contains the Schur algebra as a subalgebra. In this talk, we find a basis of the alternating Schur algebra in terms of bipartite graphs. We see a combinatorial interpretation of the structure constants of the alternating Schur algebra with respect to this basis. What additional structure does being a module for the alternating Schur algebra impose on a module for the Schur algebra? Our answer to this question involves the Koszul duality functor of Krause, and leads to a simple interpretation of his functor. Krause’s work implies that de- rived Koszul duality is an equivalence when n ≥ d. Our combinatorial methods prove the converse. This is a joint work with Amritanshu Prasad and Geetha Thangavelu.