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Adventures in categorification
by
Mikhail Khovanov
Columbia University
This is an overview which starts with an old work of the author and moves on to exciting more recent constructions of Chuang-Rouquier, Lauda, Webster, and Zheng. We'll start with the induction and restriction functors between nilCoxeter algebras and show how they categorify the first Weyl algebra. Enlarging the algebra to the nilHecke algebra allows to categorify an integral version of the positive half of quantum sl(2). Forming cyclotomic quotients leads to categorification of irreducible representations of quantum sl(2). Finally, a distributed version of the cyclotomic quotients produces a categorification of tensor products of irreducible sl(2) representations.
Date received: November 30, 2009
Copyright © 2009 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cazp-14.