Abstract
We study the structure of Yangians of affine type and deformed double current algebras, which are deformations of the enveloping algebras of matrix W 1 + ∞ -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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