MIT Infinite Dimensional Algebra Seminar

Speaker: Andrei Negut (MIT Mathematics)

Title: Generators and relations for quantum loop groups

Abstract: I will describe a program that uses shuffle algebras to yield generators-and-relations presentations for quantum loop groups. The main idea is that the necessary relations are dual to the so-called wheel conditions that describe the shuffle algebras in question, and we will use this to get a complete presentation of two interesting algebras that arise in geometric representation theory: K-theoretic Hall algebras of quivers, and Hall algebras of coherent sheaves on curves over finite fields (the latter project joint work with Francesco Sala and Olivier Schiffmann).