Affine Yangians and deformed double current algebras in type A |
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Authors: | Nicolas Guay |
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Institution: | Laboratoire de mathématiques, Université de Versailles-Saint Quentin en Yvelines, 45, avenue des États-Unis, 78035 Versailles cedex, France |
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Abstract: | We study the structure of Yangians of affine type and deformed double current algebras, which are deformations of the enveloping algebras of matrix W1+∞-algebras. We prove that they admit a PBW-type basis, establish a connection (limit construction) between these two types of algebras and toroidal quantum algebras, and we give three equivalent definitions of deformed double current algebras. We construct a Schur-Weyl functor between these algebras and rational Cherednik algebras. |
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Keywords: | Quantum algebras Yangians Cherednik algebras Poincaré -Birkhoff-Witt basis Schur-Weyl functor |
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