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

Abstract

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.

v2: Minor corrections

References in corpus (3)

• The degenerate affine walled Brauer algebra
• Affine walled Brauer algebras
• Highest weight vectors of mixed tensor products of general linear Lie superalgebras

Cited by in corpus (22)

• On the definition of quantum Heisenberg category
• The marked Brauer category
• Frobenius Heisenberg categorification
• Representations of the oriented skein category
• Heisenberg and Kac-Moody categorification
• The degenerate Heisenberg category and its Grothendieck ring
• The degenerate affine walled Brauer algebra
• Semisimplification of the category of tilting modules for GL_n
• A basis theorem for the degenerate affine oriented Brauer-Clifford supercategory
• Presentations of linear monoidal categories and their endomorphism algebras
• The affine VW supercategory
• The quantum isomeric supercategory
• Affine oriented Frobenius Brauer categories
• Diagrammatics for $F_4$
• Diagrammatics for real supergroups
• Representations of weakly triangular categories
• The spin Brauer category
• Categorical actions and multiplicities in the Deligne category $\underline{Rep}(G{L}_t)$
• Affine Frobenius Brauer Categories
• Frobenius W-algebras and traces of Frobenius Heisenberg categories
• Representations of cyclotomic oriented Brauer categories
• The disoriented skein and iquantum Brauer categories