To any finite group Γ⊂ Sp (V) of automorphisms of a symplectic vector space V we associate
a new multi-parameter deformation, H κ of the algebra ℂ V# Γ, smash product of Γ with the …

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 …

New integrable generalizations of Calogero-Moser quantum problem - Enlighten Publications
Skip to main content Accessibility information Site navigation Study Research About us Student …

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 …

The space of m-harmonic polynomials related to a Coxeter group G and a multiplicity
function m on its root system is defined as the joint kernel of the properly gauged invariant …

We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W.
Unlike in the Coxeter case, the space of quasi-invariants of a given multiplicity is not, in …

0. Introduction. This paper begins a series of papers whose goal is to establish a
representation-theoretic interpretation of the quantum Knizhnik-Zamolodchikov-Bernard …

A new class of linear second order hyperbolic partial differential operators satisfying
Huygens' principle in Minkowski spaces is presented. The construction reveals a direct …

This paper is devoted to a systematic study of quantum completely integrable systems (ie,
complete systems of commuting differential operators) from the point of view of algebraic …