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Knots in Washington XXVII; 3rd Japan-USA Workshop in Knot Theory
January 9-11, 2009
George Washington University
Washington, DC, USA

Organizers
Yoshiyuki Ohyama (TWCU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Kouki Taniyama (Waseda and GWU), Tatsuya Tsukamoto (Osaka IT), Hao Wu (GWU), Akira Yasuhara (Tokyo GU)

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A categorification of Hecke algebras
by
Alex Hoffnung
University of California, Riverside
Coauthors: John Baez

Given a Dynkin diagram and the finite field Fq, where q is a prime power, we get a finite algebraic group Gq. We will show how to construct a categorification of the Hecke algebra H(Gq) associated to this data. This is an example of the Baez/Dolan program of "Groupoidification", a method of promoting vector spaces to groupoids and linear operators to spans of groupoids. For example, given the A2 Dynkin diagram, for which Gq = SL(3, q), the spans over the Gq-set of complete flags in Fq3 encode the relations of the Hecke algebra associated to SL(3, q). Further, we will see how the categorified Yang-Baxter equation is derived from incidence relations in projective plane geometry.

Date received: November 24, 2008

Copyright © 2008 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 # caxq-30.