Evaluation 2-functors for categorified affine sl(n)

Abstract: When studying representations of particularly unruly mathematical structures, it can often be useful to compose representations of an associated, simpler structure with an `evaluation' functor from the unruly structure to the better behaved one. A previously studied example is the evaluation functor from (the idempotented universal enveloping algebra of) affine type sl(n) to finite type sl(n). In this talk I will explain this example in detail. I will then present the categorification of this evaluation functor between the corresponding 2-Kac-Moody algebras for the n=3 case, and also discuss some of the techniques used for an inductive construction of the evaluation 2-functor for larger n. This is joint work with Marco Mackaay and Pedro Vaz.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.