Quantum Topology


Full-Text PDF (1682 KB) | Metadata | Table of Contents | QT summary
Volume 8, Issue 1, 2017, pp. 113–203
DOI: 10.4171/QT/88

Published online: 2017-03-23

Categorifications of the extended affine Hecke algebra and the affine $q$-Schur algebra $\widehat {\mathbf S} (n,r)$ for $3 \leq r < n$

Marco Mackaay[1] and Anne-Laure Thiel[2]

(1) Universidade do Algarve, Faro, Portugal
(2) University of Uppsala, Sweden

We categorify the extended affine Hecke algebra and the affine quantum Schur algebra $\widehat {\mathbf S} (n,r)$ for $3 \leq r < n$, using results on diagrammatic categorification in affine type A by Elias–Williamson, that extend the work of Elias–Khovanov for finite type A, and Khovanov–Lauda respectively. We also define 2-representations of these categorifications on an extension of the 2-category of affine (singular) Soergel bimodules. These results are the affine analogue of the results in [28].

Keywords: Categorification, affine Hecke algebras, quantum algebra

Mackaay Marco, Thiel Anne-Laure: Categorifications of the extended affine Hecke algebra and the affine $q$-Schur algebra $\widehat {\mathbf S} (n,r)$ for $3 \leq r < n$. Quantum Topol. 8 (2017), 113-203. doi: 10.4171/QT/88