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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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 …

It is shown that the deformed Calogero–Moser–Sutherland (CMS) operators can be
described as the restrictions on certain affine subvarieties (called generalised discriminants) …

A special class of solutions to the generalised WDVV equations related to a finite set of
covectors is investigated. Some geometric conditions on such a set which guarantee that the …

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 …

The correspondence between the integrability of classical mechanical systems and their
quantum counterparts is not 1-1, although some close relationships exist. If a classical …

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

In this elementary paper we prove that the extra vanishing property characterizes the BC
interpolation Macdonald polynomials inside a very general class of multivariate interpolation …

An elementary construction of the eigenfunctions for the quantum rational Ruijsenaars
model with integer coupling parameter is presented. As a by-product, we establish the …