SPECIAL MIT Infinite Dimensional Algebra Seminar

Speaker: Michela Varagnolo (Université de Cergy-Pontoise)

Title: K theoretic Hall algebras and coherent categorification of quantum groups

Abstract: I will explain an isomorphism between the positive half o a quantum toroidal group and the K-theoretic Hall algebra of a preprojective algebra of affine type. There is an analogue result in the finite type case. For type $A_1$ this allows to propose a coherent categorification of the quantum affine $sl(2)$. Surprisingly it may be computed using KLR algebras. The talk is based on two joint works, one with E. Vasserot, the other with P. Shan and E. Vasserot.