A generalization of the alcove model and its applications
The alcove model of the first author and Postnikov describes highest weight crystals of semisimple Lie algebras. We present a generalization, called the quantum alcove model, and conjecture that it uniformly describes tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted a...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2012-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3090/pdf |
| _version_ | 1797270278395396096 |
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| author | Cristian Lenart Arthur Lubovsky |
| author_facet | Cristian Lenart Arthur Lubovsky |
| author_sort | Cristian Lenart |
| collection | DOAJ |
| description | The alcove model of the first author and Postnikov describes highest weight crystals of semisimple Lie algebras. We present a generalization, called the quantum alcove model, and conjecture that it uniformly describes tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types. We prove the conjecture in types $A$ and $C$. We also present evidence for the fact that a related statistic computes the energy function. |
| first_indexed | 2024-04-25T02:01:44Z |
| format | Article |
| id | doaj.art-55d0ad0229f44b56bfb6e808444aa0c9 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:44Z |
| publishDate | 2012-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-55d0ad0229f44b56bfb6e808444aa0c92024-03-07T14:51:45ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502012-01-01DMTCS Proceedings vol. AR,...Proceedings10.46298/dmtcs.30903090A generalization of the alcove model and its applicationsCristian Lenart0Arthur Lubovsky1Department of Mathematics and Statistics [Albany-USA]Department of Mathematics and Statistics [Albany-USA]The alcove model of the first author and Postnikov describes highest weight crystals of semisimple Lie algebras. We present a generalization, called the quantum alcove model, and conjecture that it uniformly describes tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types. We prove the conjecture in types $A$ and $C$. We also present evidence for the fact that a related statistic computes the energy function.https://dmtcs.episciences.org/3090/pdfenergy functionkirillov-reshetikhin crystalsalcove modelquantum bruhat graphkashiwara-nakashima columns[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Cristian Lenart Arthur Lubovsky A generalization of the alcove model and its applications Discrete Mathematics & Theoretical Computer Science energy function kirillov-reshetikhin crystals alcove model quantum bruhat graph kashiwara-nakashima columns [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | A generalization of the alcove model and its applications |
| title_full | A generalization of the alcove model and its applications |
| title_fullStr | A generalization of the alcove model and its applications |
| title_full_unstemmed | A generalization of the alcove model and its applications |
| title_short | A generalization of the alcove model and its applications |
| title_sort | generalization of the alcove model and its applications |
| topic | energy function kirillov-reshetikhin crystals alcove model quantum bruhat graph kashiwara-nakashima columns [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/3090/pdf |
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