Resumen de Affine Yangians and deformed double current algebras in type A

Nicolas Guay

• We study the structure of Yangians of affine type and deformed double current algebras, which are deformations of the enveloping algebras of matrix W1+8-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.