## University of Sydney Algebra Seminar

# Evgeny Mukhin (IUPUI)

## Friday 11 May, 12:05-12:55pm, Carslaw 175

### Minimal affinizations

I will discuss finite-dimensional representations of quantum affine algebras. In type \(A\) we have an important family of the evaluation modules which play an important role in the theory of Integrable Systems. In other types the evaluation map does not exist, and one defines a certain class of “minimal possible” modules which serve as substitutes for the evaluation representations. These modules are called minimal affinizations. I will discuss various attempts to understand the structure of the minimal affinizations including recursive relations (extended \(T\)-systems), combinatorics (via \(q\)-characters) and Weyl type conjectures (affinizations of Verma modules). This talk is based on joint papers with C.A.S. Young.