Date: Friday, October 20, 2017
Location: 1866 East Hall (3:00 PM to 4:00 PM)
Title: Quantum Groups and Categorical Quantum sl2 Actions
Abstract: 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 finitedimensional 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.
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Speaker: Nicholas Wawrykow
Institution: University of Michigan
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