Conference abstracts

Session S08 - Lie Groups and Representations

July 28, 18:10 ~ 18:30

## Tensor products of minimal affinizations in type $A$

### Aeronautics Institute of Technology, Brazil   -   fpereira@ita.br

For a quantum affine algebra of type $A$, we describe the irreducible factors of the tensor product of a general minimal affinization with a Kirillov-Reshetikhin module associated to an extreme node of the Dynkin diagram of the underlying simple Lie algebra. More precisely, we give conditions on the Drinfeld polynomials for the tensor product of the corresponding irreducible modules to be irreducible. In the reducible case we show that the product has exactly two factors and describe them.

Joint work with Adriano Moura (Universidade Estadual de Campinas, Brazil) and David Hernandez (Université Paris-Diderot Paris 7, France).