Crystallizing the algebra of functions on a compact semisimple Lie group

Abstract: The theory of crystal bases is a means of simplifying the representation theory of semisimple Lie algebras by passing through quantum groups. Varying the parameter q of the quantized enveloping algebras, 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 crystallize into purely combinatorial data described by crystal graphs. In this talk, we will describe what happens to the algebra of continuous functions on a compact semisimple Lie group under the crystallization process, yielding higher-rank graph algebras. This is joint work with Marco Matassa.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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