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| HAL: hal-00417495, version 1 |
| arXiv: 0909.2954 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2009-09-16) | v2 (2010-02-04) | v3 (2010-02-04) | v4 (2010-10-15) |
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| Factorization of the canonical bases for higher level Fock spaces |
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| Susumu Ariki 1Nicolas Jacon 2 |
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| (2010) |
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| The level l Fock space admits canonical bases G_e and G_\infty. They correspond to U_{v}(hat{sl}_{e}) and U_{v}(sl_{\infty})-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in N[v]. Restriction to the highest weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki-Koike algebras. |
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| 1: | Research Institute for Mathematical Sciences (RIMS) |
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Kyoto University |
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| 2: | Laboratoire de Mathématiques (LM-Besançon) |
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CNRS : UMR6623 – Université de Franche-Comté |
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| 3: | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| Subject | : | Mathematics/Representation Theory |
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| canonical basis – Hecke algebra – Schur algebras – decomposition matrix. |
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| hal-00417495, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00417495 | |
| oai:hal.archives-ouvertes.fr:hal-00417495 | |
| From: Nicolas Jacon | |
| Submitted on: Wednesday, 16 September 2009 10:01:22 | |
| Updated on: Thursday, 4 February 2010 11:04:50 | |
