A diagrammatic categorification of the q-Schur algebra

2010/08/07 by Marco Mackaay, Mackaay, Marco, Marko Stošić +3 · 5 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1008.1348

Abstract

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.

Cited by

• Yangians and degenerate affine Schur algebras
• Annular Evaluation and Link Homology
• Trace and categorical sl(n) representations
• Polynomial link invariants and quantum algebras
• Action of the Witt algebra on categorified quantum groups

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