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

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

Algebro-geometric Schrödinger operators in many dimensions | Philosophical Transactions of
the Royal Society A: Mathematical, Physical and Engineering Sciences logo logo Skip main …

Several algebro-geometric properties of commutative rings of partial differential operators
(PDOs) as well as several geometric constructions are investigated. In particular, we show …

A natural generalization is given for the classification of commutative rings of ordinary
differential operators, as presented by Krichever, Mumford, Mulase. The commutative rings …

In this paper, we study properties of the algebras of planar quasi‐invariants. These algebras
are Cohen–Macaulay and Gorenstein in codimension one. Using the technique of matrix …

We introduce a class of hyperplane arrangements A in C n that generalise the locus
configurations of Chalykh, Feigin and Veselov. To such an arrangement we associate a …

We investigate further algebro-geometric properties of commutative rings of partial
differential operators, continuing our research started in previous articles. In particular, we …

The super-Jack polynomials, introduced by Kerov, Okounkov and Olshanski, are
polynomials in n+ m variables, which reduce to the Jack polynomials when n= 0 or m= 0 and …

We study a class of arrangements of lines with multiplicities on the plane which admit the
Chalykh–Veselov Baker–Akhiezer function. These arrangements are obtained by adding …