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Representation Theory

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Soergel calculus


Authors: Ben Elias and Geordie Williamson
Journal: Represent. Theory 20 (2016), 295-374
MSC (2010): Primary 20C33, 20F55, 20G05; Secondary 22E46
DOI: https://doi.org/10.1090/ert/481
Published electronically: October 7, 2016
MathSciNet review: 3555156
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Abstract: 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
Email: belias@uoregon.edu

Geordie Williamson
Affiliation: Max-Planck-Institut für Mathematik, 53111 Bonn, Germany
Email: geordie@mpim-bonn.mpg.de

DOI: https://doi.org/10.1090/ert/481
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
Article copyright: © Copyright 2016 by the authors