Constructs an action of the positive Witt algebra on categorified quantum groups for simply-laced Lie algebras, recovering the foam action in type A and inducing the current-algebra action via trace decategorification.
A diagrammatic categorification of the q-Schur algebra
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In this paper we categorify the q-Schur algebra S(n,d) as a quotient of Khovanov and Lauda's diagrammatic 2-category U(sln). We also show that our 2-category contains Soergel's monoidal category of bimodules of type A, which categorifies the Hecke algebra H(d), as a full sub-2-category if d does not exceed n. For the latter result we use Elias and Khovanov's diagrammatic presentation of Soergel's monoidal category of type A.
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Action of the Witt algebra on categorified quantum groups
Constructs an action of the positive Witt algebra on categorified quantum groups for simply-laced Lie algebras, recovering the foam action in type A and inducing the current-algebra action via trace decategorification.