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Letters in Mathematical Physics, ISSN 0377-9017, 10/2016, Volume 106, Issue 10, pp. 1429 - 1449
We present a direct construction of compact real forms of the trigonometric and elliptic $${n}$$ n -particle Ruijsenaars–Schneider systems whose completed... 
Geometry | 37J35 | 37J15 | Theoretical, Mathematical and Computational Physics | 70H06 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | Ruijsenaars–Schneider models | compact phase space | Physics | integrable systems | MAPS | Ruijsenaars-Schneider models | CALOGERO-MOSER SYSTEMS | MODEL | PHYSICS, MATHEMATICAL
Journal Article
Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2015, Volume 51, Issue 2, pp. 273 - 288
We compute the Bernstein Sato polynomial of f, a function which given a pair (M, upsilon) in X = M-n(C) x C-n tests whether upsilon is a cyclic vector for M.... 
Calogero-Moser | Bernstein-Sato polynomial | Cyclic pair | b-function | PREHOMOGENEOUS VECTOR-SPACES | MATHEMATICS | cyclic pair | Bernstein Sato polynomial | SYSTEMS
Journal Article
Nuclear Physics, Section B, ISSN 0550-3213, 12/2019, Volume 949, p. 114807
We present generalizations of the well-known trigonometric spin Sutherland models, which were derived by Hamiltonian reduction of ‘free motion’ on cotangent... 
DEGENERATE INTEGRABILITY | CALOGERO-MOSER SYSTEMS | SPACES | PHYSICS, PARTICLES & FIELDS
Journal Article
Journal of Algebra, ISSN 0021-8693, 09/2016, Volume 462, pp. 197 - 252
The goal of this paper is to compute the cuspidal Calogero–Moser families for all infinite families of finite Coxeter groups, at all parameters. We do this by... 
Complex reflection groups | Cherednik algebras | Symplectic leaves | Hecke algebras | Calogero–Moser spaces | Calogero-Moser spaces | SPACE | MATHEMATICS | SYMPLECTIC REFLECTION ALGEBRAS | PARTITION | SUBGROUPS | G(M | RATIONAL CHEREDNIK ALGEBRAS | Family | Algebra
Journal Article
Selecta Mathematica, ISSN 1022-1824, 05/2009, Volume 14, Issue 3, pp. 373 - 396
Journal Article
Compositio Mathematica, ISSN 0010-437X, 11/2008, Volume 144, Issue 6, pp. 1403 - 1428
We present a simple description of moduli spaces of torsion-free D-modules (D-bundles) on general smooth complex curves, generalizing the identification of the... 
Calogero-Moser spaces | D-modules | Koszul duality | Perverse coherent sheaves | perverse coherent sheaves | MATHEMATICS | ALGEBRAS | RIGHT IDEALS | CATEGORIES | MODULI
Journal Article
CONDENSED MATTER PHYSICS, ISSN 1607-324X, 2019, Volume 22, Issue 3, p. 33101
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 04/2015, Volume 56, Issue 4, p. 42703
The superintegrability of four Hamiltonians (H-r) over tilde = lambda H-r, r = a, b, c, d, where H-r are known Hamiltonians and lambda is a certain function... 
CALOGERO-MOSER SYSTEM | NONCONSTANT CURVATURE | 3-DIMENSIONAL EUCLIDEAN-SPACE | NONLINEAR OSCILLATOR | CONSTANT-CURVATURE | SPHERE | SMORODINSKY-WINTERNITZ POTENTIALS | HYPERBOLIC PLANE | DRACH | PHYSICS, MATHEMATICAL | CURVED SPACES | Hamiltonian functions | Parameters | Deformation
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2017, Volume 50, Issue 11, p. 115203
We present a construction of a new integrable model as an infinite limit of Calogero models of N particles with spin. It is implemented in the multicomponent... 
vertex operators | multicomponent Fock space | Yangian | Calogero-Moser system | Dunkl operators | SUTHERLAND MODEL | PHYSICS, MULTIDISCIPLINARY | MATRIX MODELS | PHYSICS, MATHEMATICAL | OPERATORS
Journal Article
NONLINEARITY, ISSN 0951-7715, 11/2019, Volume 32, Issue 11, pp. 4377 - 4394
We investigate the finite dimensional dynamical system derived by Braden and Hone in 1996 from the solitons of A(n-1) affine Toda field theory. This system of... 
MATHEMATICS, APPLIED | SPACES | bi-Hamiltonian systems | Hamiltonian reduction | spin Ruijsenaars-Schneider-Sutherland models | DEGENERATE INTEGRABILITY | CALOGERO-MOSER SYSTEMS | PHYSICS, MATHEMATICAL | integrable systems | GEOMETRY
Journal Article
St. Petersburg Mathematical Journal, ISSN 1061-0022, 2011, Volume 22, Issue 3, pp. 463 - 472
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2014, Volume 397, pp. 209 - 224
We study the Dunkl–Opdam subalgebra of the rational Cherednik algebra for wreath products at t=0, and use this to describe the block decomposition of... 
Dunkl–Opdam subalgebras | Blocks | Cherednik algebras | Dunkl-Opdam subalgebras | MATHEMATICS | CALOGERO-MOSER SPACE | Algebra
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2011, Volume 44, Issue 35, pp. 353001 - 47
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2013, Volume 46, Issue 12, pp. 125206 - 9
The higher order superintegrability of separable potentials is studied. It is proved that these potentials possess (in addition to the two quadratic integrals)... 
CALOGERO-MOSER SYSTEM | 3-DIMENSIONAL EUCLIDEAN-SPACE | MOTION | SYMMETRIES | CONSTANTS | PHYSICS, MULTIDISCIPLINARY | CLASSICAL MECHANICS | 3RD-ORDER INTEGRALS | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | Functions (mathematics) | Integrals | Mathematical analysis | Proving | Paper | Constants | Harmonic oscillators
Journal Article
Electronic Research Announcements in Mathematical Sciences, ISSN 1935-9179, 2011, Volume 18, pp. 12 - 21
We describe the structure of the automorphism groups of algebras Morita equivalent to the first Weyl algebra A(1)(k). In particular, we give a geometric... 
Automorphism groups | Calogero-Moser spaces | Dixmier conjecture | Weyl algebras | Bass-Serre theory | MATHEMATICS | AUTOMORPHISMS | automorphism groups | IDEALS | Dixmier Conjecture
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2004, Volume 186, Issue 1, pp. 1 - 57
We establish a connection between smooth symplectic resolutions and symplectic deformations of a (possibly singular) affine Poisson variety. In particular, let... 
Calogero–Moser space | McKay correspondence | Poisson deformations | Calogero-Moser space | INVARIANTS | MATHEMATICS | COHOMOLOGY | MODULES | REFLECTION ALGEBRAS | RING | WEYL ALGEBRA | FINITE-GROUP | MANIFOLDS | HOMOLOGY
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 12/2019, Volume 22, Issue 6, pp. 1533 - 1567
The representation theory of rational Cherednik algebras of type A at t = 0 gives rise, by considering supports, to a natural family of smooth Lagrangian... 
Associative Rings and Algebras | Rational Cherednik algebras | Primary 14E15 | Schubert calculus | Non-associative Rings and Algebras | Secondary 14E30, 16S80, 17B63 | Commutative Rings and Algebras | Representation theory | Mathematics | Adelic Grassmanian | Calogero-Moser space | MATHEMATICS | VERMA MODULES
Journal Article
Selecta Mathematica, ISSN 1022-1824, 1/2016, Volume 22, Issue 1, pp. 111 - 144
We define uniformly the notions of Dirac operators and Dirac cohomology in the framework of the Hecke algebras introduced by Drinfeld (Anal i Prilozhen... 
Mathematics, general | Mathematics | 20C08 | 20F55 | DISCRETE SERIES | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | OPERATOR | AFFINE HECKE ALGEBRAS | CALOGERO-MOSER SPACE | SYSTEMS | RATIONAL CHEREDNIK ALGEBRAS | CHARACTERS | Algebra
Journal Article
Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, 04/2020, Volume 27, Issue 2, pp. 243 - 266
Sklyanin's formula provides a set of canonical spectral coordinates on the standard Calogero-Moser space associated with the quiver consisting of a vertex and... 
Calogero-Moser | 37J15 | 14H70 | cyclic quiver | Darboux coordinates | 53D20 | Sklyanin's formula | canonical spectral coordinates | MATHEMATICS, APPLIED | VARIETIES | SYSTEMS | PHYSICS, MATHEMATICAL | GEOMETRY
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2012, Volume 8, p. 072
We discuss a relation between the characteristic variety of the KZ equations and the zero set of the classical Calogero-Moser Hamiltonians. 
Wronski map | Calogero-Moser system | Gaudin Hamiltonians | SPACE | ALGEBRA | EQUATIONS | PHYSICS, MATHEMATICAL | VECTOR
Journal Article
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