A basis theorem for the affine oriented Brauer category and its cyclotomic quotients

Jonathan Brundan, Jonathan Comes, David Nash, Andrew Reynolds

Published 2014-04-25, updated 2014-07-20Version 2

The affine oriented Brauer category is a monoidal category obtained from the oriented Brauer category (= the free symmetric monoidal category generated by a single object and its dual) by adjoining a polynomial generator subject to appropriate relations. In this article, we prove a basis theorem for the morphism spaces in this category, as well as for all of its cyclotomic quotients.