798 citations · 3.1k across the 77 of their papers we have counts for
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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…