483 citations · 1.7k across the 181 of their papers we have counts for
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On spectral theory of quantum vertex operators
Pavel Etingof
In this note we prove the Davies-Foda-Jimbo-Miwa-Nakayashiki conjecture on the asymptotics of the composition of n quantum vertex operators for the quantum affine algebra U_q(\hat…
Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials
Pavel Etingof, Alexander Kirillov
This paper is a continuation of our papers \cite{EK1, EK2}. In \cite{EK2} we showed that for the root system one can obtain Macdonald's polynomials as weighted traces of…
Representations of tensor categories and Dynkin diagrams
Pavel Etingof, Mikhail Khovanov
In this note we illustrate by a few examples the general principle: interesting algebras and representations defined over Z_+ come from category theory, and are best understood whe…
Spherical functions on affine Lie groups
Pavel Etingof, Igor Frenkel, Alexander Kirillov
We describe vector valued conjugacy equivariant functions on a group K in two cases -- K is a compact simple Lie group, and K is an affine Lie group. We construct such functions as…
Integral formulas for wave functions of quantum many-body problems and representations of gl(n)
Pavel Etingof
We derive explicit integral formulas for eigenfunctions of quantum integrals of the Calogero-Sutherland-Moser operator with trigonometric interaction potential. In particular, we d…
Algebraic integrability of Schrödinger operators and representations of Lie algebras
Pavel Etingof, Kostantin Styrkas
In this paper we study integrability and algebraic integrability properties of certain matrix Schrödinger operators. More specifically, we associate such an operator (with rational…