This article is an extended version of the minicourse given by the second author at the summer school of the conference Interactions of quantum affine algebras with cluster algebras, current algebras and catego
We establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the ( q , t )-characters of certain irreducible representations, among which ...
$Q$-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They can also be viewed as mutations in certain cluster algebras, which have a natural quantum deformati
Cluster algebras form an axiomatically defined class of commutative rings designed to serve as an algebraic framework for the theory of total positivity and canonical bases in semisimple groups and their quantum analogs. In this paper we introduce and study quantum deformations of cluster algebras. ...
Middle Lecture Room, Math Building讲座论坛简介 In this talk, I will give an introduction of the cluster algebras arising from the representation theory of quantum affine algebras. I will construct a common triangular basis of such a cluster algebra, which is parametrized by the tropical points. ...
Leclerc, Cluster algebras and quantum affine algebras, Duke Math. J. 154, no. 2 (2010): 265-341.David Hernandez, Bernard Leclerc, Cluster algebras and quantum affine algebras, Duke Math. Journal 154 (2) (2010) 265-341.HERNANDEZ D; LECLERC B.Cluster algebras and quantum affine algebras....
We establish ring isomorphisms between quantum Grothendieck rings of certain remarkable monoidal subcategories of finite-dimensional representations of quantum affine algebras of types $A_{2n-1}^{(1)}$ and $B_n^{(1)}$. Our proof relies in part on the corresponding quantum cluster algebra ...
cluster algebrasThe T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently they were generalized to quantum affinizations of quantum Kac-Moody algebras associated with a wide class of generalized Cartan matrices which we say ...
A quantum cluster algebra approach to representations of simply laced quantum affine algebrasLea Bittmann
Q-systems are recursion relations satisfied by the characters of the restrictions of special finite-dimensional modules of quantum affine algebras. They can also be viewed as mutations in certain cluster algebras, which have a natural quantum deformation. In this paper, we explain the relation in ...