A diagrammatic categorification of the -Schur algebra
Marco Mackaay
Universidade do Algarve, Faro, PortugalMarko Stošić
Instituto Superior Técnico, Lisboa, PortugalPedro Vaz
Instituto Superior Técnico, Lisboa, Portugal
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Abstract
In this paper we categorify the q-Schur algebra as a quotient of Khovanov and Lauda’s diagrammatic 2-category (Khovanov and Lauda 2010). We also show that our 2-category contains Soergel’s (1992) monoidal category of bimodules of type , which categorifies the Hecke algebra , as a full sub-2-category if . For the latter result we use Elias and Khovanov’s diagrammatic presentation of Soergel’s monoidal category of type ; see (Elias and Khovanov, 2009).
Cite this article
Marco Mackaay, Marko Stošić, Pedro Vaz, A diagrammatic categorification of the -Schur algebra. Quantum Topol. 4 (2013), no. 1, pp. 1–75
DOI 10.4171/QT/34