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Crystals, coboundary categories, and the moduli space of points on RP1.
Algebra & Discrete Mathematics| Speaker: | Joel Kamnitzer, UC Berkeley |
| Location: | 593 Kerr |
| Start time: | Fri, May 7 2004, 4:10PM |
Description
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. This
commutor is symmetric but does not satisfy the usual hexagon axiom.
Instead it obeys a different axiom which makes the category of crystals
into 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 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.