JournalsqtVol. 4, No. 1pp. 1–75

A diagrammatic categorification of the <var>q</var>-Schur algebra

  • Marco Mackaay

    Universidade do Algarve, Faro, Portugal
  • Marko Stošić

    Instituto Superior Técnico, Lisboa, Portugal
  • Pedro Vaz

    Instituto Superior Técnico, Lisboa, Portugal
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Abstract

In this paper we categorify the q-Schur algebra Sq(n,d)\mathbf{S}_q(n,d) as a quotient of Khovanov and Lauda’s diagrammatic 2-category U(sln)\mathcal{U}(\mathfrak{sl}_n) [16]. We also show that our 2-category contains Soergel’s [33] monoidal category of bimodules of type AA, which categorifies the Hecke algebra Hq(d)H_q(d), as a full sub-2-category if dnd\leq n. For the latter result we use Elias and Khovanov’s diagrammatic presentation of Soergel’s monoidal category of type AA; see [8].

Cite this article

Marco Mackaay, Marko Stošić, Pedro Vaz, A diagrammatic categorification of the <var>q</var>-Schur algebra. Quantum Topol. 4 (2013), no. 1, pp. 1–75

DOI 10.4171/QT/34