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

Abstract

We categorify the extended affine Hecke algebra and the affine quantum Schur algebra $\hat{\mathbf{S}}(n,r)$ for $3\le r<n$, 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].