Abstract CONTENTS Introduction Chapter I. Integrable Lagrange systems with discrete time
§ 1. Hamiltonian theory of Lagrange systems with discrete time § 2. Discrete analogues of …

Abstract CONTENTS Introduction Chapter I. Hadamard's criterion and the Painlevé property
Chapter II. Solution of the Hadamard problem in the four-dimensional Minkowski space § …

We develop representation theory of the rational Cherednik algebra \rmH\sbc associated to
a finite Coxeter group W in a vector space h, and a parameter" c." We use it to show that, for …

We consider here the coexistence of first-and third-order integrals of motion in two-
dimensional classical and quantum mechanics. We find explicitly all potentials that admit …

We define a system of 'dynamical'differential equations compatible with the KZ differential
equations. The KZ differential equations are associated to a complex simple Lie algebra g …

Abstract The deformed quantum Calogero-Moser-Sutherland problems related to the root
systems of the contragredient Lie superalgebras are introduced. The construction is based …

New integrable generalizations of Calogero-Moser quantum problem - Enlighten Publications
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We discuss the problem of exhaustive enumeration of all possible factorization for a given
linem ordinary differential operator. A theoretical investigation of topological and …

A notion of the rational Baker–Akhiezer (BA) function related to a configuration of
hyperplanes in C n is introduced. It is proved that the BA function exists only for very special …

We show that the partially spherical cyclotomic rational Cherednik algebra (obtained from
the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying …