Coproduct for Yangians of affine Kac–Moody algebras

Affine Yangians and deformed double current algebras in type A

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 PBWtype 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 ...

Twisted Yangians, Twisted Quantum Loop Algebras and Affine Hecke Algebras of Type Bc

We study twisted Yangians of type AIII which have appeared in the literature under the name of reflection algebras. They admit q-versions which are new twisted quantum loop algebras. We explain how these can be defined equivalently either via the reflection equation or as coideal subalgebras of Yangians of gln (resp. of quantum loop algebras of gln). The connection with affine Hecke algebras of...

Cherednik algebras and Yangians

We construct a functor from the category of modules over the trigonometric (resp. rational) Cherednik algebra of type gll to the category of integrable modules of level l over a Yangian for the loop algebra sln (resp. over a subalgebra of this Yangian called the Yangian deformed double loop algebra) and we establish that it is an equivalence of categories if l + 2 < n.

Yangians and transvector algebras

Olshanski' s centralizer construction provides a realization of the Yangian Y(m) for the Lie algebra gl(m) as a subalgebra in the projective limit algebra A m = lim proj A m (n) as n → ∞, where A m (n) is the centralizer of gl(n − m) in the enveloping algebra U(gl(n)). We give a modified version of this construction based on a quantum analog of Sylvester's theorem. We then use it to get an alge...

Yangians and Classical Lie Algebras