REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: Shuffle algebras are certain constructions in quantum algebra, first introduced by Feigin and Odesskii almost 15 years ago. They provide an explicit description of quantum toroidal algebras, which are otherwise presented only by generators and relations. We will give some very explicit formulas for the Hopf structure of these shuffle algebras, as well as for the quantum affine algebras that lie inside them. These formulas have lately found applications in the categorification of certain quiver varieties, computations of knot invariants and combinatorics.