Quantum Grothendieck rings as quantum cluster algebras

Abstract

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.

Léa Bittmann

Research Associate