Mathematics Colloquia and Seminars

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Description

Let g denote a simple Lie algebra of type A, D, E. Drinfeld and Jimbo have attached to g a quantum affine algebra, which has a very rich theory of finite-dimensional representations. This has been studied by many authors over the years (Chari-Pressley, Ginzburg-Vasserot, Frenkel-Reshetikhin, Frenkel-Mukhin, Kashiwara, Nakajima, Hernandez, ...). In this talk I will present a recent joint work with Hernandez concerning the t-deformed Grothendieck ring of this category, introduced by Varagnolo-Vasserot and Nakajima. We have obtained a presentation of this ring by generators and relations, in the spirit of the familiar Drinfeld-Jimbo presentation of the positive part of the quantum enveloping algebra of g. I will explain how we derive this presentation, and how it relates to Lusztig's dual canonical basis.