Type: Seminar

Distribution: World

Expiry: 17 Nov 2024

CalTitle1: Algebra Seminar: Crystallizing Functions on Compact Lie Groups

Auth: alexs@pa49-180-194-107.pa.nsw.optusnet.com.au (ashe8718) in SMS-SAML

Robert Yuncken (Universite de Lorraine) will speak in the algebra seminar this week. We will go out for lunch after the talk. When: 12-1pm Friday 13, September Where: 275 Carslaw Title: Crystallizing Functions on Compact Lie Groups Abstract: The theory of crystal bases is a means of simplifying the representation theory of semisimple Lie algebras by passing through quantum groups. Specifically, varying the parameter q of a quantized enveloping algebra, we pass from the classical theory at q=1 through the Drinfeld-Jimbo algebras at 0 < q < 1 to the crystal limit at q=0. At q=0, the main features of the representation theory crystallize into purely combinatorial data described by crystal graphs. In this talk I will explain what happens in the dual world of function algebras on compact quantum groups, yielding k-graph algebras in the sense of Kumjian-Pask. This generalizes, in part, work by Woronowicz, Hong-Szymanski and Giselsson. (Joint work with Marco Matassa.)