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Quantum Topology


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Volume 8, Issue 1, 2017, pp. 75–112
DOI: 10.4171/QT/87

Published online: 2017-03-23

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

Jonathan Brundan[1], Jonathan Comes[2], David Nash[3] and Andrew Reynolds[4]

(1) University of Oregon, Eugene, USA
(2) The College of Idaho, Caldwell, USA
(3) Le Moyne College, Syracuse, USA
(4) University of Oregon, Eugene, USA

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.

Keywords: Affine oriented Brauer category, affine walled Brauer algebra

Brundan Jonathan, Comes Jonathan, Nash David, Reynolds Andrew: A basis theorem for the affine oriented Brauer category and its cyclotomic quotients. Quantum Topol. 8 (2017), 75-112. doi: 10.4171/QT/87