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Trigonometric and Elliptic Ruijsenaars–Schneider Systems on the Complex Projective Space

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

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

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

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

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

In these notes, we give a survey of the main results of [5] and [7]. Our aim is to generalize the geometric classification of (left) ideals of the first Weyl...

Calogero–Moser space | Rings of difierential operators | perverse sheaves | preprojective algebras | Mathematics, general | Mathematics | representation varieties | Secondary 16G20, 14H60, 18E30 | recollement | Primary 16S32, 16S38 | Perverse sheaves | Representation varieties | Preprojective algebras | Recollement | Calogero-Moser space | Rings of differential operators | MATHEMATICS, APPLIED | MATHEMATICS | RIGHT IDEALS | DEFORMATIONS | WEYL ALGEBRA | DIFFERENTIAL-OPERATORS | KLEINIAN SINGULARITIES | GEOMETRY

Calogero–Moser space | Rings of difierential operators | perverse sheaves | preprojective algebras | Mathematics, general | Mathematics | representation varieties | Secondary 16G20, 14H60, 18E30 | recollement | Primary 16S32, 16S38 | Perverse sheaves | Representation varieties | Preprojective algebras | Recollement | Calogero-Moser space | Rings of differential operators | MATHEMATICS, APPLIED | MATHEMATICS | RIGHT IDEALS | DEFORMATIONS | WEYL ALGEBRA | DIFFERENTIAL-OPERATORS | KLEINIAN SINGULARITIES | GEOMETRY

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

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

There is developed a current algebra representation scheme for reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock...

SPACE | quantum symmetries | PHYSICS, CONDENSED MATTER | Fock space | Calogero-Moser-Sutherlan model | quantum integrability | OPERATORS | Bogolubov generating functional | LOCAL CURRENT-ALGEBRA | current algebra representations | Hamiltonian reconstruction | Operators (mathematics) | Current algebra | One dimensional models | Representations | Dynamical systems | Nonlinear systems | Symmetry

SPACE | quantum symmetries | PHYSICS, CONDENSED MATTER | Fock space | Calogero-Moser-Sutherlan model | quantum integrability | OPERATORS | Bogolubov generating functional | LOCAL CURRENT-ALGEBRA | current algebra representations | Hamiltonian reconstruction | Operators (mathematics) | Current algebra | One dimensional models | Representations | Dynamical systems | Nonlinear systems | Symmetry

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

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

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

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

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

A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding...

PHYSICS, MULTIDISCIPLINARY | ANNIHILATION-CREATION OPERATORS | SHAPE-INVARIANT POTENTIALS | ASKEY-WILSON POLYNOMIALS | GENERAL POTENTIALS | ONE-DIMENSIONAL EXAMPLES | ORTHOGONAL POLYNOMIALS | COHERENT STATES | CALOGERO-MOSER SYSTEMS | EXACTLY-SOLVABLE PROBLEMS | PHYSICS, MATHEMATICAL | POSCHL-TELLER POTENTIALS | Pictures | Algebra | Solution space | Mathematical analysis | Quantum mechanics | Polynomials | Schroedinger equation | Symmetry

PHYSICS, MULTIDISCIPLINARY | ANNIHILATION-CREATION OPERATORS | SHAPE-INVARIANT POTENTIALS | ASKEY-WILSON POLYNOMIALS | GENERAL POTENTIALS | ONE-DIMENSIONAL EXAMPLES | ORTHOGONAL POLYNOMIALS | COHERENT STATES | CALOGERO-MOSER SYSTEMS | EXACTLY-SOLVABLE PROBLEMS | PHYSICS, MATHEMATICAL | POSCHL-TELLER POTENTIALS | Pictures | Algebra | Solution space | Mathematical analysis | Quantum mechanics | Polynomials | Schroedinger equation | Symmetry

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

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

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

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

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

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

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

Wronski map | Calogero-Moser system | Gaudin Hamiltonians | SPACE | ALGEBRA | EQUATIONS | PHYSICS, MATHEMATICAL | VECTOR

Journal Article

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