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| HAL: hal-00349853, version 3 |
| arXiv: 0901.0443 |
| Detailed view |  Export this paper |
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| Pacific Journal of Mathematics 243, No.2 (2009) 287-311 |
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| Available versions: | v1 (2009-01-05) | v2 (2009-03-03) | v3 (2009-04-22) |
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| Kashiwara and Zelevinsky involutions in affine type A |
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| Nicolas Jacon 1Cédric Lecouvey 2 |
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| (2009) |
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| We first describe how the Kashiwara involution on crystals of affine type $A$ is encoded by the combinatorics of aperiodic multisegments. This yields a simple relation between this involution and the Zelevinsky involution on the set of simple modules for the affine Hecke algebras. We then give efficient procedures for computing these involutions. Remarkably, these procedures do not use the underlying crystal structure. They also permit to match explicitly the Ginzburg and Ariki parametrizations of the simple modules associated to affine and cyclotomic Hecke algebras, respectively . |
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| 1: | Laboratoire de Mathématiques (LM-Besançon) |
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CNRS : UMR6623 – Université de Franche-Comté |
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| 2: | Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville (LMPA) |
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Université du Littoral Côte d'Opale : EA2597 |
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| Subject | : | Mathematics/Representation Theory Mathematics/Combinatorics Mathematics/Quantum Algebra |
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| hal-00349853, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00349853 | |
| oai:hal.archives-ouvertes.fr:hal-00349853 | |
| From: Nicolas Jacon | |
| Submitted on: Wednesday, 22 April 2009 10:21:13 | |
| Updated on: Tuesday, 20 April 2010 16:10:42 | |
