483 citations · 1.7k across the 181 of their papers we have counts for
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Macdonald's polynomials and representations of quantum groups
Pavel Etingof, Alexander Kirillov
In this paper we present a formula for Macdonald's polynomials for the root system A(n-1) which arises from the representation theory of quantum sl(n). This formula expresses Macdo…
A unified representation-theoretic approach to special functions
Pavel Etingof, Alexander Kirillov
A representation-theoretic approach to special functions was developed in the 40-s and 50-s in the works of I.M.Gelfand, M.A.Naimark, N.Ya.Vilenkin, and their collaborators. The es…
Difference equations with elliptic coefficients and quantum affine algebras
Pavel Etingof
The purpose of this paper is to introduce and study a q-analogue of the holonomic system of differential equations associated to the Belavin's classical r-matrix (elliptic r-matrix…
Quantum integrable systems and representations of Lie algebras
Pavel Etingof
In this paper the quantum integrals of the Hamiltonian of the quantum many-body problem with the interaction potential K/sinh^2(x) (Sutherland operator) are constructed as images o…
Representations of affine Lie algebras, parabolic differential equations, and Lame functions
Pavel Etingof, Alexander Kirillov
We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of t…
Quantum Knizhnik-Zamolodchikov equations and holomorphic vector bundles
Pavel Etingof
The paper introduces a new geometric interpretation of the quantum Knizhnik-Zamolodchikov equations introduced in 1991 by I.Frenkel and N.Reshetikhin. It turns out that these equat…