Speaker
Bob Yuncken
Description
The structure theory of the finite dimensional representations of a quantized enveloping algebra undergoes a massive simplification when the deformation parameter q goes to 0. This is the fundamental observation in the theory of crystal bases of Kashiwara and Lusztig. On might ask if there is a similar simplification of the Pontrjagin dual, meaning a crystallisation of the quantized algebra of functions on a compact semisimple Lie group. The answer is that the crystal limit is a combinatorial algebra associated to symbolic dynamics. I will describe this crystal limit, as well as its analogue for the noncompact group SL(2,C).
(Joint work with Marco Matassa and Aidan Sims.)