**Title:** Crystals, coboundary categories, and the moduli space of points on RP1

**Speaker:** Joel Kamnitzer

**Speaker Info:** Berkeley

**Brief Description:**

**Special Note**:

**Abstract:**

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.

Copyright © 1997-2024 Department of Mathematics, Northwestern University.