Student Representation Theory Seminar

In the 1980s Drinfeld and Jimbo independently arrived on the concept of a quantum group, a class of Hopf algebras. By deforming the Serre relations of the universal enveloping algebra of a symmetrizable Lie algebra one gets a quantum group. The quantum group arising from a semisimple Lie algebra acts on the weight spaces of its irreducible finite-dimensional representations in a manner similar to its nondeformed counterpart. One can categorify these representations, lifting the action of the quantum group to a categorical action on the resulting categorified representation. In this talk I will present an overview of quantum groups, before focusing on the simplest case: quantum sl2. Additionally, I will discuss the action of quantum sl2 on its categorified representations looking towards next week's seminar.
Speaker(s): Nicholas Wawrykow (University of Michigan)