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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.)