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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Soergel calculus
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by Ben Elias and Geordie Williamson PDF
Represent. Theory 20 (2016), 295-374


The monoidal category of Soergel bimodules is an incarnation of the Hecke category, a fundamental object in representation theory. We present this category by generators and relations, using the language of planar diagrammatics. We show that Libedinsky’s light leaves give a basis for morphism spaces and give a new proof and a generalization of Soergel’s classification of the indecomposable Soergel bimodules.
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Additional Information
  • Ben Elias
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • MR Author ID: 896756
  • Email:
  • Geordie Williamson
  • Affiliation: Max-Planck-Institut für Mathematik, 53111 Bonn, Germany
  • MR Author ID: 845262
  • Email:
  • Received by editor(s): January 16, 2015
  • Received by editor(s) in revised form: March 24, 2016
  • Published electronically: October 7, 2016
  • Additional Notes: The first-named author was supported by NSF Postdoctoral Fellowship DMS-1103862

  • Dedicated: To Mikhail Khovanov and Raphaël Rouquier, who taught us generators and relations
  • © Copyright 2016 by the authors
  • Journal: Represent. Theory 20 (2016), 295-374
  • MSC (2010): Primary 20C33, 20F55, 20G05; Secondary 22E46
  • DOI:
  • MathSciNet review: 3555156