A remark on BMW algebra, q-Schur algebras and categorification

TL;DR

This paper establishes embeddings of BMW algebras into algebras related to knot polynomials and q-Schur algebras, and constructs their categorifications, advancing the understanding of algebraic structures in knot theory.

Contribution

It proves embeddings of BMW algebras into HOMFLY-PT related algebras and q-Schur algebras, and develops their categorifications, linking knot invariants and algebraic categorification.

Findings

BMW algebra embeds into HOMFLY-PT algebra

so(2N)-BMW algebra embeds into q-Schur algebra of type A

Constructs categorifications of the so(2N)-BMW algebra

Abstract

We prove that the 2-variable BMW algebra embeds into an algebra constructed from the HOMFLY-PT polynomial. We also prove that the so(2N)-BMW algebra embeds in the q-Schur algebra of type A. We use these results to construct categorifications of the so(2N)-BMW algebra.