Seminar Event Detail


Combinatorics

Date:  Friday, December 06, 2013
Location:  3866 East Hall (4:10 PM to 5:00 PM)

Title:  Stable representation theory

Abstract:   The theory of polynomial representations of the infinite general
linear group is closely related to several other
representation-theoretic topics, such as symmetric functions, Schur
functors, and symmetric groups. It is natural to try to relax
"polynomial" to "rational" and retain a similar theory. Koike and
Terada worked out the symmetric function version of this. One of the
new phenomena they encountered was that specializing a (rational)
Schur function to a (rational) symmetric polynomial can give the
negative of a (rational) Schur polynomial. I will explain recent work
with Steven Sam where we fill in the categorical aspects of this
theory. We define a category of rational representations of the
infinite general linear group, and relate it to several other
representation-theoretic topics, such as the Koike--Terada theory,
rational Schur functors, walled Brauer algebras, and twisted
commutative algebras, the last of which has no interesting analog in
the polynomial theory. Unlike the polynomial theory, this category is
not semi-simple, and this explains the negative sign in the
Koike--Terada rule: it is the manifestation of a higher derived
functor.

Files:


Speaker:  Andrew Snowden
Institution:  U. Michigan

Event Organizer:     

 

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