798 citations · 3.1k across the 77 of their papers we have counts for
25 papers · 1 filter
Weyl group symmetry of q-characters
Edward Frenkel, David Hernandez
We define an action of the Weyl group W of a simple Lie algebra g on a completion of the ring Y, which is the codomain of the q-character homomorphism of the corresponding quantum…
Quantum Langlands duality of representations of W-algebras
Tomoyuki Arakawa, Edward Frenkel
We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands Program and some related results.
Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
Edward Frenkel, David Hernandez
We prove a system of relations in the Grothendieck ring of the category O of representations of the Borel subalgebra of an untwisted quantum affine algebra U_q(g^) introduced in [H…
Baxter's Relations and Spectra of Quantum Integrable Models
Edward Frenkel, David Hernandez
Generalized Baxter's relations on the transfer-matrices (also known as Baxter's TQ relations) are constructed and proved for an arbitrary untwisted quantum affine algebra. Moreover…
Soliton equations, vertex operators, and simple singularities
E. Frenkel, A. Givental, T. Milanov
We prove the equivalence of two hierarchies of soliton equations associated to a simply-laced finite Dynkin diagram. The first was defined by Kac and Wakimoto using the principal r…
Langlands duality for finite-dimensional representations of quantum affine algebras
Edward Frenkel, David Hernandez
We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9…
Langlands duality for representations of quantum groups
Edward Frenkel, David Hernandez
We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-si…
On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level
Boris Feigin, Edward Frenkel, Leonid Rybnikov
We present an independent short proof of the main result of arXiv:0706.3725 that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of fun…
Opers with irregular singularity and spectra of the shift of argument subalgebra
Boris Feigin, Edward Frenkel, Leonid Rybnikov
The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras math.RT/0606380, math.QA…
Local Geometric Langlands Correspondence: the Spherical Case
Edward Frenkel, Dennis Gaitsgory
A module over an affine Kac--Moody algebra g^ is called spherical if the action of the Lie subalgebra g[[t]] on it integrates to an algebraic action of the corresponding group G[[t…
Weyl modules and opers without monodromy
Edward Frenkel, Dennis Gaitsgory
We prove that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with regula…
Quantization of soliton systems and Langlands duality
Boris Feigin, Edward Frenkel
We consider the problem of quantization of classical soliton integrable systems, such as the KdV hierarchy, in the framework of a general formalism of Gaudin models associated to a…
Gaudin models with irregular singularities
B. Feigin, E. Frenkel, V. Toledano-Laredo
We introduce a class of quantum integrable systems generalizing the Gaudin model. The corresponding algebras of quantum Hamiltonians are obtained as quotients of the center of the…
Ramifications of the geometric Langlands Program
Edward Frenkel
The global geometric Langlands correspondence relates Hecke eigensheaves on the moduli stack of G-bundles on a smooth projective algebraic curve X and holomorphic G'-bundles with c…
Gaudin model and opers
Edward Frenkel
This is a review of our previous works (some of them joint with B. Feigin and N. Reshetikhin) on the Gaudin model and opers. We define a commutative subalgebra in the tensor power…
Self-extensions of Verma modules and differential forms on opers
Edward Frenkel, Constantin Teleman
We compute the algebras of self-extensions of the vacuum module and the Verma modules over an affine Kac-Moody algebra g^ in suitable categories of Harish-Chandra modules. We show…
Opers on the projective line, flag manifolds and Bethe Ansatz
Edward Frenkel
We consider the problem of diagonalization of the hamiltonians of the Gaudin model, which is a quantum chain model associated to a simple Lie algebra. The hamiltonians of this mode…
Affine Kac-Moody algebras, integrable systems and their deformations
Edward Frenkel
This is the text of the Hermann Weyl Prize lecture given by the author at the XXIV Colloquium on Group Theoretical Methods in Physics, Paris, July 2002 (to appear in the Proceeding…
Lectures on Wakimoto modules, opers and the center at the critical level
Edward Frenkel
Wakimoto modules are representations of affine Kac-Moody algebras in Fock modules over infinite-dimensional Heisenberg algebras. In these lectures we present the construction of th…
The Hopf algebra
Edward Frenkel, Evgeny Mukhin
We define the Hopf algebra structure on the Grothendieck group of finite-dimensional polynomial representations of in the limit . The resulting Hopf…
The q-characters at roots of unity
Edward Frenkel, Evgeny Mukhin
We consider various specializations of the non-twisted quantum affine algebras at roots of unity. We define and study the q-characters of their finite-dimensional representations.
Vertex Algebras and Algebraic Curves
Edward Frenkel
This is the text of the Bourbaki seminar that I gave on June 24, 2000.
Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
Edward Frenkel, Evgeny Mukhin
We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from math.QA/9810055 and derive some of their corollaries. In pa…
Integrable Hierarchies and Wakimoto Modules
Boris Feigin, Edward Frenkel
In our earlier papers we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theo…