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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.

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Face functors for KLR algebras
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by Peter J. McNamara and Peter Tingley PDF
Represent. Theory 21 (2017), 106-131 Request permission


Simple representations of KLR algebras can be used to realize the infinity crystal for the corresponding symmetrizable Kac-Moody algebra. It was recently shown that, in finite and affine types, certain sub-categories of “cuspidal” representations realize crystals for sub-Kac-Moody algebras. Here we put that observation on a firmer categorical footing by exhibiting a corresponding functor between the category of representations of the KLR algebra for the sub-Kac-Moody algebra and the category of cuspidal representations of the original KLR algebra.
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Additional Information
  • Peter J. McNamara
  • Affiliation: School of Mathematics and Physics, University of Queensland, St Lucia, QLD, Australia
  • MR Author ID: 791816
  • Email:
  • Peter Tingley
  • Affiliation: Department of Mathematics and Statistics, Loyola University, Chicago, Illinois 60660
  • MR Author ID: 679482
  • Email:
  • Received by editor(s): February 12, 2016
  • Received by editor(s) in revised form: October 3, 2016, March 13, 2017, and May 1, 2017
  • Published electronically: July 12, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Represent. Theory 21 (2017), 106-131
  • MSC (2010): Primary 17B37
  • DOI:
  • MathSciNet review: 3670026