Abstract

Using the Brundan-Kleshchev isomorphism between symmetric group algebras and KLR algebras of type A , the algebra was studied extensively. However, there is relatively little known about KLR algebras of other types. In this talk, we derive the first results about homomorphisms between Specht modules over KLR algebras of type C. First, we describe the action of some of the generators on the basis elements of the Specht module when is a hook with a short arm, i.e. it has length less than . Then we explicitly describe the homomorphisms between and and give an outline of our proof. Finally, we generalise James's well-known result for the trivial module and describe all shapes such that . This is joint work with Martin Forsberg Conde.

 

Organizers: Harry Richman (NCTS), Wille Liu (AS)