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Factorization of the canonical bases for higher level Fock spaces

Abstract : 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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Submitted on : Friday, October 15, 2010 - 8:14:38 AM
Last modification on : Tuesday, August 28, 2018 - 7:48:02 AM
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Susumu Ariki, Nicolas Jacon, Cédric Lecouvey. Factorization of the canonical bases for higher level Fock spaces. Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP), 2012, 55, pp.23-51. ⟨10.1017/S0013091510000519⟩. ⟨hal-00417495v4⟩

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