Face functors for KLR algebras

McNamara, Peter; Tingley, Peter

doi:10.1090/ert/496

Face functors for KLR algebras
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by Peter J. McNamara and Peter Tingley

Represent. Theory 21 (2017), 106-131

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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