| Type de publication : |
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Preprint, Working Paper, Document sans référence, etc. |
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| Domaine : |
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| Titre : |
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Cyclotomic Hecke algebras: Jucys-Murphy elements, representations, classical limit |
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| Auteur(s) : |
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Oleg Ogievetsky 1, 2, Loic Poulain D'Andecy ( ) 1, 2 |
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| Laboratoire : |
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| Résumé : |
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An inductive approach to the representation theory of cyclotomic Hecke algebras, inspired by Okounkov and Vershik, is developed. We study the common spectrum of the Jucys-Murphy elements using representations of the simplest affine Hecke algebra. Representations are constructed with the help of a new associative algebra whose underlying vector space is the tensor product of the cyclotomic Hecke algebra with the free associative algebra generated by standard m-tableaux. The classical limit of the whole approach, including the construction of representations, is given. The flatness of the deformation is proved without the use of the representation theory. |
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Langue du texte
intégral : |
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Anglais |
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Date de production,
écriture : |
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01/11/2011 |
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| Mots Clés : |
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Hecke algebras – complex reflection groups – Jucys-Murphy elements – flat deformations – Young diagrams – Young tableaux – Bratteli diagrams |
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| Commentaire : |
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91 p. |
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