A diagrammatic categorification of the affine $q$-Schur algebra $\hat{\mathbold{S}}(n,n)$ for $n \geq 3$

Marco Mackaay and Anne-Laure Thiel

Vol. 278 (2015), No. 1, 201–233

DOI: 10.2140/pjm.2015.278.201

Abstract

This is a follow-up to our 2013 paper “Categorifications of the extended affine Hecke algebra and the affine quantum Schur algebra $\hat{S}\left(n,r\right)$ for $3\le r<n$” in which we categorified the affine $q$-Schur algebra $\hat{S}\left(n,r\right)$ for $2<r<n$ using a quotient of the categorification of $U_q\left({\widehat{\mathfrak{s}l}}_n\right)$ of Khovanov and Lauda (2009, 2010, 2011). In this paper we categorify $\hat{S}\left(n,n\right)$ for $n\ge 3$ using an extension of the aforementioned quotient.

Keywords

categorification, affine Schur algebras, quantum algebra

Mathematical Subject Classification 2010

Primary: 17B37, 16T99

Milestones

Received: 22 July 2014

Revised: 5 March 2015

Accepted: 16 March 2015

Published: 30 September 2015