Algebra Seminar

Title: Crystals, coboundary categories, and the moduli space of points on RP1
Speaker: Joel Kamnitzer
Speaker Info: Berkeley
Brief Description:
Special Note:

A crystal for a representation of a semisimple Lie algebra is a combinatorial object which encodes the structure of the representation. There is an interesting tensor product on these crystals. We give a construction of a commutor (natural isomophisms A x B -> B x A) for the category of crystals of a semisimple Lie algebra. With this commutor, the category of crystals is not a braided category. Rather it is an example of an analogous notion which is called a coboundary category.

Motivated by the above construction, we investigate the structure of coboundary categories. Just as the braid group acts on repeated tensor products in a braided category, the fundamental group of the moduli space of stable real genus 0 curves with n marked points acts on repeated tensor products in a coboundary category.

Date: Tuesday, November 02, 2004
Time: 4:10pm
Where: Lunt 104
Contact Person: Prof. Kari Vilonen
Contact email: vilonen@math.northwestern.edu
Contact Phone: 847-491-5557
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