Geometric Methods in Representation Theory Seminar
Steven Sam, UC Berkeley
What 


When 
Mar 08, 2013 from 04:00 PM to 05:00 PM 
Where  Phillips Hall 367 
Contact Name  Shrawan Kumar 
Add event to calendar 
vCal iCal 
Title: Homology of Littlewood complexes
Abstract: The universal character ring of KoikeTerada allows one to calculate with the character theory of "infinite rank" classical groups similar to how one uses the ring of symmetric functions in infinitely many variables to calculate with the character theory of the infinite general linear group. For this to be useful, one needs a specialization map to usual character rings. This has the strange property that an irreducible character specializes either to 0 or plus or minus an irreducible character. We explain this by showing that this is the combinatorial shadow of the behavior of the derived functors of a left exact functor from a category of representations of an infinite rank classical group to the category of representations of a finite rank classical group. The calculation of these derived functors uses the BorelWeilBott theorem in a nondirect way and connects to some classical invariant theory. I will explain some examples and how these different ingredients are connected. This is based on joint work with Andrew Snowden and Jerzy Weyman.