University of Sydney Algebra Seminar
Robert Yuncken
Friday 13 September, 12-1pm, Place: Carslaw 275
Crystallizing Functions on Compact Lie Groups
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.)