Cherednik algebras and Yangians
نویسنده
چکیده
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.
منابع مشابه
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 ...
متن کاملApplications of Procesi Bundles to Cherednik Algebras
In this talk we describe some applications of Procesi bundles that appeared in Gufang’s talk to type A Rational Cherednik algebras introduced in Jose’s talk. We start by recalling Procesi bundles, quantum Hamiltonian reductions, and Cherednik algebras. Then we apply Procesi bundles to relating the spherical Rational Cherednik algebras to quantum Hamiltonian reductions. Finally, we study the def...
متن کاملTwisted 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...
متن کاملDrinfeld J Presentation of Twisted Yangians
We present a quantization of a Lie coideal structure for twisted half-loop algebras of finite-dimensional simple complex Lie algebras. We obtain algebra closure relations of twisted Yangians in Drinfeld J presentation for all symmetric pairs of simple Lie algebras and for simple twisted even half-loop Lie algebras. We provide the explicit form of the closure relations for twisted Yangians in Dr...
متن کاملFrom quantum loop algebras to Yangians
The main purpose of this note is to give a proof of a statement of V. Drinfeld in [Dr1] regarding Yangians and quantum loop algebras, namely how the former can be constructed as limit forms of the latter. We also apply the same ideas to twisted quantum loop algebras to recover the (non-twisted) Yangians.
متن کامل