A diagrammatic categorification of the q-schur algebra

Abstract

In this paper we categorify the q-Schur algebra S<inf>q</inf>(n, d) as a quotient of Khovanov and Lauda’s diagrammatic 2-category U(sl<inf>n</inf>) [16]. We also show that our 2-category contains Soergel’s [33]monoidal category of bimodules of type A, which categorifies the Hecke algebra H<inf>q</inf>(d), as a full sub-2-category if d ≤ n. For the latter result we use Elias and Khovanov’s diagrammatic presentation of Soergel’s monoidal category of type A; see [8].