Quiver Yangians and -algebras for generalized conifolds

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

A geometric construction of generalized quiver Hecke algebras

We provide a common generalization of the Springer map and quiver-graded Springer map due to Lusztig, called generalized quiver-graded Springer map associated to generalized quiver representations introduced by Derksen and Weyman. Following Chriss and Ginzburg for any equivariant projective map π : E → V , there is an algebra structure on the equivariant Borel-Moore homology of Z = E ×V E, we c...

Quiver Schur Algebras for the Linear Quiver I

We define a graded quasi-hereditary covering for the cyclotomic quiver Hecke algebras Rn of type A when e = 0 (the linear quiver) or e ≥ n. We show that these algebras are quasi-hereditary graded cellular algebras by giving explicit homogeneous bases for them. When e = 0 we show that the KLR grading on the quiver Hecke algebras is compatible with the gradings on parabolic category OΛ n previous...