#### Vol. 278, No. 1, 2015

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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
##### Abstract

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