SMS scnews item created by Anthony Henderson at Fri 19 Sep 2008 1446
Type: Seminar
Distribution: World
Expiry: 26 Sep 2008
Calendar1: 26 Sep 2008 1205-1255
CalLoc1: Carslaw 159
CalTitle1: Algebra Seminar: Morrison -- Generators and relations for the representation theory of U_q(sl_n) as a planar algebra
Auth: anthonyh@asti.maths.usyd.edu.au

Algebra Seminar

Generators and relations for the representation theory of U_q(sl_n) as a planar algebra

Scott Morrison

26th September, 12:05-12:55pm, Carslaw 159


Abstract

I'll begin by explaining what a planar algebra is, and then show you how the representation theory of SU(2) and SU(3) can be given a "finite presentation by generators and relations" as a planar algebra. This may be familiar to some, as the Temperley-Lieb algebra for SU(2) or Kuperberg's spider for SU(3). Next, I'll explain my work on generalising this to all SU(n). We'll start with a category of diagrams, generated by some trivalent vertices, and a surjective map to the representation theory; the difficulty will be understanding the relations amongst these diagrams. The main trick is to remember that SU(n) sits inside SU(n+1), and conversely representations of SU(n+1) break up (or "branch") as representations of SU(n). I'll explain how to understand the combinatorics of branching in terms of my diagrams, and how to use this to "lift" relations for diagrams from one level to the next.


After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

Anthony Henderson anthonyh@maths.usyd.edu.au.



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