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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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
Represent. Theory 20 (2016), 295-374
Published electronically: October 7, 2016


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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Bibliographic 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