Volodymyr Mazorchuk: Mini-Course
s30.06.2015-08.07.2015
Organisiert von: A. Beliakova
4 lectures
June 30, July 3, July 6, July 8, 10:00-12:00, room Y27H28
Categorification of U_q-modules
Abstract: In this series of lectures we plan to describe how one categorifies simple finite dimensional modules over a quantum group U_q. We start with an outline of basic representation theory for U_q. Then we will address the algebraic background of the term categorification. The aim is then to give explicit categorification of simple finite diemnsional U_q-modules. All steps will be illustrated by detailed examples.
Required background:
basics of representation theory for associative algebras and Lie algebras; basic category theory and higher category theory; basic topology
Literature:
- Mazorchuk, Volodymyr: Lectures on algebraic categorification. QGM Master Class Series. European Mathematical Society (EMS), Zürich, 2012
- Mazorchuk, Volodymyr: Lectures on sl_2(C)-modules. Imperial College Press, London, 2010.
- Leinster, Tom: Basic Bicategories. arXiv:math/9810017
- Frenkel, Igor; Khovanov, Mikhail; Stroppel, Catharina: A categorification of finite-dimensional irreducible representations of quantum sl2 and their tensor products. Selecta Math. (N.S.) 12 (2006), no. 3-4, 379–431.
- Mazorchuk, Volodymyr; Stroppel, Catharina: A combinatorial approach to functorial quantum sl_k knot invariants. Amer. J. Math. 131 (2009), no. 6, 1679–1713.