University of Sydney Algebra Seminar

Travis Scrimshaw

Friday 21 August, 12-1pm, in Carslaw 275

Denominator formulas for KR modules in nonexceptional types

The finite dimensional representations of quantum affine algebras is a rich topic with many remarkable structures and connections to other areas of mathematics and physics. Generically, the tensor product of two representations is irreducible, but a fundamental question is to determine when they are not (in which case it generally remains indecomposable). This is governed by the denominator formula for the R-matrix, where the roots are the points where the tensor product is not irreducible. Hence, we need to compute the denominator formula. In this talk, after introducing the necessary background, we describe the denominator formula for the class of Kirillov-Reshetikhin modules in all nonexceptional types, where we require new higher level versions of the Dorey’s rule morphisms. This is based on joint work with Se-jin Oh.