A Basis Theorem for the Degenerate Affine Oriented Brauer–Clifford Supercategory

Abstract

AbstractWe introduce the oriented Brauer–Clifford and degenerate affine oriented Brauer–Clifford supercategories. These are diagrammatically defined monoidal supercategories that 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.