It is known that some Grothendieck rings of categories of representations of quantum affine algebras can be endowed with cluster algebras structures. This is true for example for certain categories O containing the category of finite-dimensional representations. On the other hand, certain Grothendieck rings of categories of finite dimensional representations admit remarkable t-deformations, which are linked to quiver varieties and are useful to compute characters. In this work, we define a quantum Grothendieck ring for the category O as a quantum cluster algebra, this gives a new algorithm to compute characters.

Date

Jun 7, 2019

Location

RIMS

Kyoto, Japan