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 Ŝ(n,r) for 3 r < n” in which we categorified the affine q-Schur algebra Ŝ(n,r) for 2 < r < n using a quotient of the categorification of Uq(sl̂n) of Khovanov and Lauda (2009, 2010, 2011). In this paper we categorify Ŝ(n,n) for n 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
Authors
Marco Mackaay
Center for Mathematical Analysis, Geometry, and Dynamical Systems
Departamento de Matemática
Instituto Superior Técnico
1049-001 Lisboa
Portugal
Departamento de Matemática
FCT
Universidade do Algarve
Campus de Gambelas
8005-139 Faro
Portugal
Anne-Laure Thiel
Matematiska Institutionen
Uppsala Universitet
75106 Uppsala
Sweden