Mathematics

Cherednik algebras, Yangians and deformed double current algebras I

Nicolas Guay (UIUC Math)

Abstract: I will start by quickly recalling the different generalizations of the classical Schur-Weyl duality between $\mathfrak&ob;sl&cb;_n$ and the symmetric group $S_l$. Afterwards, I will define (trigonometric, rational) Cherednik algebras and Yangians of finite and affine type. I will describe some recent results on the theme of Schur-Weyl duality involving these algebras. The Schur-Weyl functor can be used to understand the structure of affine Yangians and deformed double-current algebras, a new class of algebras introduced in the second part of my talk. For instance, one application is the construction of PBW-bases for these algebras. I will also explain how deformed double-current algebras can be viewed as limit forms of affine Yangians and how to define them in three different ways. I will end by mentioning briefly two possible avenues for future research on this subject.