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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| Format: | Article |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6388/pdf |
| _version_ | 1797270216133050368 |
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| author | Henry Kvinge Monica Vazirani |
| author_facet | Henry Kvinge Monica Vazirani |
| author_sort | Henry Kvinge |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:00:44Z |
| format | Article |
| id | doaj.art-8e4a69fcb2d444658c8b734433ec681f |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:44Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-8e4a69fcb2d444658c8b734433ec681f2024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63886388Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystalHenry Kvinge0https://orcid.org/0000-0003-4108-1364Monica Vazirani1Department of Mathematics [Univ California Davis]Department of Mathematics [Univ California Davis]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.https://dmtcs.episciences.org/6388/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Henry Kvinge Monica Vazirani Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal |
| title_full | Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal |
| title_fullStr | Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal |
| title_full_unstemmed | Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal |
| title_short | Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal |
| title_sort | categorifying the tensor product of the kirillov reshetikhin crystal b1 1 and a fundamental crystal |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6388/pdf |
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