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Représentations des algèbres affinisées quantiques : q,t-caractères et produit de fusion

Abstract : In this thesis we propose several new developments in the study of quantum groups and their representations. In the framework of the study of finite dimensional representations of quantum affine algebras, we give a new and more general algebraic construction of q,t-characters (t-deformations of Frenkel-Reshetikhin's q-characters), independent from the geometric construction of Nakajima (which holds only in the ADE-case). It allows us to extend the quantization of the Grothendieck ring and the definition of analogs of Kazhdan-Lusztig polynomials to non simply laced cases. Besides we establish a triangular decomposition of general quantum affinizations (including quantum affine and toroidal algebras) and classify their integrable highest weight representations. We propose a new construction of a fusion product by defining a deformation of the ``new Drinfel'd coproduct''.
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Contributor : David Hernandez <>
Submitted on : Friday, October 22, 2004 - 6:16:59 PM
Last modification on : Thursday, December 10, 2020 - 12:36:47 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:07:53 PM


  • HAL Id : tel-00007188, version 1


David Hernandez. Représentations des algèbres affinisées quantiques : q,t-caractères et produit de fusion. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2004. Français. ⟨tel-00007188⟩



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