A proof of Comes-Kujawa's conjecture

TL;DR

This paper proves Comes-Kujawa's conjecture regarding a basis for the cyclotomic oriented Brauer-Clifford supercategory and establishes an isomorphism between two related superalgebras over certain fields.

Contribution

It provides a proof of the conjecture on the basis of the supercategory and shows the equivalence of two cyclotomic superalgebras under specific conditions.

Findings

Confirmed the basis conjecture for the supercategory.

Established isomorphism between two cyclotomic superalgebras.

Extended understanding of the algebraic structure over algebraically closed fields.

Abstract

Let $\kappa$ be a commutative ring containing $2^{-1}$. In this paper, we prove the Comes-Kujawa's conjecture on a $\kappa$-basis of cyclotomic oriented Brauer-Clifford supercategory. As a by-product, we prove that the cyclotomic walled Brauer-Clifford superalgebra defined by Comes and Kujawa and ours are isomorphic if $\kappa$ is an algebraically closed field with characteristic not two.