Prelegent: ROBERT YUNCKEN
The theory of crystal bases, due to Kashiwara and Lusztig, 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 this point, the main features of the representation theory (matrix coefficients, Clebsch-Gordan coefficients, branching rules) crystallize into purely combinatorial data described by crystal graphs. In this talk, we will describe what happens to the *-algebra of functions on a compact semisimple Lie group under the crystallization process, leading to a higher-rank graph algebra. This generalizes, in part, work by Woronowicz, Hong and Szymański, and Giselsson. (Joint work with Marco Matassa.)
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