Deformed quantum Calogero-Moser problems and Lie superalgebras
AN Sergeev, AP Veselov - Communications in mathematical physics, 2004 - Springer
Abstract The deformed quantum Calogero-Moser-Sutherland problems related to the root
systems of the contragredient Lie superalgebras are introduced. The construction is based …
systems of the contragredient Lie superalgebras are introduced. The construction is based …
Generalised discriminants, deformed Calogero–Moser–Sutherland operators and super-Jack polynomials
AN Sergeev, AP Veselov - Advances in Mathematics, 2005 - Elsevier
It is shown that the deformed Calogero–Moser–Sutherland (CMS) operators can be
described as the restrictions on certain affine subvarieties (called generalised discriminants) …
described as the restrictions on certain affine subvarieties (called generalised discriminants) …
Algebro-geometric Schrödinger operators in many dimensions
O Chalykh - … Transactions of the Royal Society A …, 2008 - royalsocietypublishing.org
Algebro-geometric Schrödinger operators in many dimensions | Philosophical Transactions of
the Royal Society A: Mathematical, Physical and Engineering Sciences logo logo Skip main …
the Royal Society A: Mathematical, Physical and Engineering Sciences logo logo Skip main …
Commuting differential operators and higher-dimensional algebraic varieties
H Kurke, D Osipov, A Zheglov - Selecta Mathematica, 2014 - Springer
Several algebro-geometric properties of commutative rings of partial differential operators
(PDOs) as well as several geometric constructions are investigated. In particular, we show …
(PDOs) as well as several geometric constructions are investigated. In particular, we show …
On rings of commuting partial differential operators
A Zheglov - St. Petersburg Mathematical Journal, 2014 - ams.org
A natural generalization is given for the classification of commutative rings of ordinary
differential operators, as presented by Krichever, Mumford, Mulase. The commutative rings …
differential operators, as presented by Krichever, Mumford, Mulase. The commutative rings …
Cohen–Macaulay modules over the algebra of planar quasi–invariants and Calogero–Moser systems
I Burban, A Zheglov - Proceedings of the London Mathematical …, 2020 - Wiley Online Library
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 …
are Cohen–Macaulay and Gorenstein in codimension one. Using the technique of matrix …
Deformed Calogero–Moser operators and ideals of rational Cherednik algebras
Y Berest, O Chalykh - Communications in Mathematical Physics, 2023 - Springer
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 …
configurations of Chalykh, Feigin and Veselov. To such an arrangement we associate a …
Geometric properties of commutative subalgebras of partial differential operators
AB Zheglov, H Kurke - Sbornik: Mathematics, 2015 - iopscience.iop.org
We investigate further algebro-geometric properties of commutative rings of partial
differential operators, continuing our research started in previous articles. In particular, we …
differential operators, continuing our research started in previous articles. In particular, we …
New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
M Hallnäs - Constructive Approximation, 2024 - Springer
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 …
polynomials in n+ m variables, which reduce to the Jack polynomials when n= 0 or m= 0 and …
A class of Baker–Akhiezer arrangements
M Feigin, D Johnston - Communications in Mathematical Physics, 2014 - Springer
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 …
Chalykh–Veselov Baker–Akhiezer function. These arrangements are obtained by adding …