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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Vydáno v:Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavní autoři: Kvinge, Henry, Vazirani, Monica
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Témata:
[math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
ISSN:1365-8050, 1462-7264, 1365-8050
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Abstract 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.
AbstractList 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.
Author Vazirani, Monica
Kvinge, Henry
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  givenname: Monica
  surname: Vazirani
  fullname: Vazirani, Monica
  organization: Department of Mathematics [Univ California Davis]
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Snippet We use Khovanov-Lauda-Rouquier (KLR) algebras to categorify a crystal isomorphism between a funda-mental crystal and the tensor product of a...
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SubjectTerms [math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
Title Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal
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