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International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 978635, 58 pages
Research Article

Diagrammatics for Soergel Categories

Department of Mathematics, Columbia University, New York, NY 10027, USA

Received 4 May 2010; Accepted 31 December 2010

Academic Editor: Alistair Savage

Copyright © 2010 Ben Elias and Mikhail Khovanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group. We present this category, when the Weyl group is the symmetric group, in the language of planar diagrams with local generators and local defining relations.