798 citations · 3.1k across the 77 of their papers we have counts for
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Five Lectures on Soliton Equations
Edward Frenkel
This is a self-contained review of a new approach to soliton equations of KdV type developed by the author together with B. Feigin and B. Enriquez.
Deformations of W-algebras associated to simple Lie algebras
Edward Frenkel, Nicolai Reshetikhin
Deformed $\W$--algebra $\W_{q,t}(\g)$ associated to an arbitrary simple Lie algebra $\g$ is defined together with its free field realizations and the screening operators. Explicit…
Towards Deformed Chiral Algebras
Edward Frenkel, Nikolai Reshetikhin
We describe a new algebraic structure of "deformed chiral algebra" motivated by the study of the deformed W-algebras. We use it to gain some insights into the deformed Virasoro alg…
Geometric interpretation of the Poisson structure in affine Toda field theories
Benjamin Enriquez, Edward Frenkel
We express the Poisson brackets of local fields of the affine Toda field theories in terms of the Drinfeld-Sokolov dressing operator. For this, we introduce a larger space of field…
Equivalence of Two Approaches to the mKdV Hierarchies
Benjamin Enriquez, Edward Frenkel
The equivalence between the approaches of Drinfeld-Sokolov and Feigin-Frenkel to the mKdV hierarchies is established. A new derivation of the mKdV equations in the zero curvature f…
Deformations of the KdV hierarchy and related soliton equations
Edward Frenkel
We define hierarchies of differential--q-difference equations, which are q-deformations of the equations of the generalized KdV hierarchies. We show that these hierarchies are biha…
Quantum W-algebras and Elliptic Algebras
Boris Feigin, Edward Frenkel
We define quantum W-algebras generalizing the results of Reshetikhin and the second author, and Shiraishi-Kubo-Awata-Odake. The quantum W-algebra associated to sl_N is an associati…
Affine Algebras, Langlands Duality and Bethe Ansatz
Edward Frenkel
We review various aspects of representation theory of affine algebras at the critical level, geometric Langlands correspondence, and Bethe ansatz in the Gaudin models. Geometric La…
Quantum Affine Algebras and Deformations of the Virasoro and W-algebras
Edward Frenkel, Nikolai Reshetikhin
We generalize some results concerning affine algebras at the critical level to the corresponding quantum algebras. In particular, we show that the Wakimoto realization provides a h…