Representation theory seminar: Skein relations for diagrammatic categories.

Seminar | October 23 | 10-11 a.m. | 939 Evans Hall

 Rina Anno, Kansas State University

 Department of Mathematics

In the category of tangles objects are even natural numbers and morphisms between n and m are (n,m)-tangles up to isotopy. Weak triangulated represenations of this category are usually constructed in terms of generators and relations: we associate a functor to each tangle generator (a "cup", a "cap", or a "crossing"), and prove that certain compositions of these functors are isomorphic. It turns out that if we impose additionally a certain skein relation, which is not intrinsic to the tangle category but requires a triangulated representation, all tangle relations follow from those that only involve cups and caps. We are going to discuss the analogue of this result for the category of $sl_n$ webs. This talk is based on joint work with Timothy Logvinenko