The octahedron recurrence and gln crystals
<p>We study the hive model of gln tensor products, following Knutson, Tao, and Woodward. We define a coboundary category where the tensor product is given by hives and where the associator and commutor are defined using a modified octahedron recurrence. We then prove that this category is equi...
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| Format: | Journal article |
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Elsevier
2006
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| _version_ | 1797063321273237504 |
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| author | Henriques, A Kamnitzer, J |
| author_facet | Henriques, A Kamnitzer, J |
| author_sort | Henriques, A |
| collection | OXFORD |
| description | <p>We study the hive model of gln tensor products, following Knutson, Tao, and Woodward. We define a coboundary category where the tensor product is given by hives and where the associator and commutor are defined using a modified octahedron recurrence. We then prove that this category is equivalent to the category of crystals for the Lie algebra gln. The proof of this equivalence uses a new connection between the octahedron recurrence and the Jeu de Taquin and Schützenberger involution procedures on Young tableaux.</p> |
| first_indexed | 2024-03-06T20:58:09Z |
| format | Journal article |
| id | oxford-uuid:39f78a2b-1860-43e5-b927-17dfce0c79d4 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:58:09Z |
| publishDate | 2006 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:39f78a2b-1860-43e5-b927-17dfce0c79d42022-03-26T13:58:42ZThe octahedron recurrence and gln crystalsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:39f78a2b-1860-43e5-b927-17dfce0c79d4Symplectic Elements at OxfordElsevier2006Henriques, AKamnitzer, J<p>We study the hive model of gln tensor products, following Knutson, Tao, and Woodward. We define a coboundary category where the tensor product is given by hives and where the associator and commutor are defined using a modified octahedron recurrence. We then prove that this category is equivalent to the category of crystals for the Lie algebra gln. The proof of this equivalence uses a new connection between the octahedron recurrence and the Jeu de Taquin and Schützenberger involution procedures on Young tableaux.</p> |
| spellingShingle | Henriques, A Kamnitzer, J The octahedron recurrence and gln crystals |
| title | The octahedron recurrence and gln crystals |
| title_full | The octahedron recurrence and gln crystals |
| title_fullStr | The octahedron recurrence and gln crystals |
| title_full_unstemmed | The octahedron recurrence and gln crystals |
| title_short | The octahedron recurrence and gln crystals |
| title_sort | octahedron recurrence and gln crystals |
| work_keys_str_mv | AT henriquesa theoctahedronrecurrenceandglncrystals AT kamnitzerj theoctahedronrecurrenceandglncrystals AT henriquesa octahedronrecurrenceandglncrystals AT kamnitzerj octahedronrecurrenceandglncrystals |