A basis theorem for the degenerate affine oriented Brauer-Clifford supercategory

Abstract

We introduce the oriented Brauer-Clifford and degenerate affine oriented Brauer-Clifford supercategories. These are diagrammatically defined monoidal supercategories which provide combinatorial models for certain natural monoidal supercategories of supermodules and endosuperfunctors, respectively, for the Lie superalgebras of type Q. Our main results are basis theorems for these diagram supercategories. We also discuss connections and applications to the representation theory of the Lie superalgebra of type Q.Comment: 37 pages, many figures. Version 3 replaces the partial results from the previous versions with a proof by the first author of a basis theorem for cyclotomic quotients at all levels. Various other minor corrections and revisions were mad