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Representation Theory

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Face functors for KLR algebras


Authors: Peter J. McNamara and Peter Tingley
Journal: Represent. Theory 21 (2017), 106-131
MSC (2010): Primary 17B37
DOI: https://doi.org/10.1090/ert/496
Published electronically: July 12, 2017
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Abstract: 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
Email: maths@petermc.net

Peter Tingley
Affiliation: Department of Mathematics and Statistics, Loyola University, Chicago, Illinois 60660
Email: ptingley@luc.edu

DOI: https://doi.org/10.1090/ert/496
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
Article copyright: © Copyright 2017 American Mathematical Society

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