Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal

We use Khovanov-Lauda-Rouquier (KLR) algebras to categorify a crystal isomorphism between a funda-mental crystal and the tensor product of a Kirillov-Reshetikhin crystal and another fundamental crystal, all in affine type. The nodes of the Kirillov-Reshetikhin crystal correspond to a family of “triv...

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Bibliographic Details
Published in:	Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 28th...
Main Authors:	Kvinge, Henry, Vazirani, Monica
Format:	Journal Article Conference Proceeding
Language:	English
Published:	DMTCS 22.04.2020 Discrete Mathematics & Theoretical Computer Science
Subjects:	[math.math-co]mathematics [math]/combinatorics [math.co] Combinatorics Mathematics
ISSN:	1365-8050, 1462-7264, 1365-8050
Online Access:	Get full text
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Summary:	We use Khovanov-Lauda-Rouquier (KLR) algebras to categorify a crystal isomorphism between a funda-mental crystal and the tensor product of a Kirillov-Reshetikhin crystal and another fundamental crystal, all in affine type. The nodes of the Kirillov-Reshetikhin crystal correspond to a family of “trivial” modules. The nodes of the fun-damental crystal correspond to simple modules of the corresponding cyclotomic KLR algebra. The crystal operators correspond to socle of restriction and behave compatibly with the rule for tensor product of crystal graphs.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.6388