Fetching the paper…
Reading the bibliography…
We establish a direct link between Dunkl operators and quantum Lax matrices $\mathcal L$ for the Calogero--Moser systems associated to an arbitrary Weyl group $W$ (or an arbitrary finite reflection group in the rational case).
P. D. Lax: Integrals of nonlinear equations of evolution and solitary waves
1968
Earlier work this paper cites.
F. Calogero, Solution of the one-dimensional N N -body problems with quadratic and/or inversely quadratic pair potentials, J. Math. Phys. 12
1971
Earlier work this paper cites.
H. Flashka: On the Toda lattice. Inverse scattering solutions
1974
Earlier work this paper cites.
F. Calogero, Exactly solvable one-dimensional many-body systems, Lett. Nuovo Cimento 13
1975
Earlier work this paper cites.
J. Moser: Three integrable Hamiltonian systems connected with isospectral deformation
1975
Earlier work this paper cites.
A. M. Perelomov: Completely integrable classical systems connected with semisimple Lie algebras. III
1977
Earlier work this paper cites.
D. Kazhdan, B. Kostant, S. Sternberg: Hamiltonian group actions and dynamical systems of Calogero type
1978
Earlier work this paper cites.
I. M. Krichever: Elliptic solutions of the Kadomtsev–Petviashvili equation and integrable systems of particles
1980
Earlier work this paper cites.
: M. A. Olshanetsky, A. M. Perelomov: Classical integrable systems related to Lie algebras
1981
Earlier work this paper cites.
M. A. Olshanetsky, A. M. Perelomov: Quantum integrable systems related to Lie algebras
1983
Earlier work this paper cites.
S. N. M. Ruijsenaars, H. Schneider: A new class of integrable systems and its relation to solitons
1986
Earlier work this paper cites.
M. Bruschi, F. Calogero: The Lax representation for an integrable class of relativistic dynamical systems
1987
Earlier work this paper cites.
S. N. M. Ruijsenaars: Complete integrability of relativistic Calogero–Moser systems and elliptic function identities
1987
Earlier work this paper cites.
Ruijsenaars, S.N.M.: Action-angle maps and scattering theory for some finite-dimensional integrable systems I. The pure soliton case
1988
Earlier work this paper cites.
C. F. Dunkl: Differential-difference operators associated to reflection groups
1989
Earlier work this paper cites.
V. Inozemtsev: Lax representation with spectral parameter on a torus for integrable particle systems
1989
Earlier work this paper cites.
I. Cherednik: A unification of Knizhnik–Zamolodchikov equations and Dunkl operators via affine Hecke algebras
1991
Earlier work this paper cites.
G. J. Heckman: A remark on the Dunkl differential-difference operators
1991
Earlier work this paper cites.
G. J. Heckman: An elementary approach to the hypergeometric shift operators of Opdam
1991
Earlier work this paper cites.
Brink, L., Hansson, T. H., Vasiliev, M. A.: Explicit solution to the N N -body Calogero problem
1992
Earlier work this paper cites.
I. Cherednik: Quantum Knizhnik–Zamolodchikov equations and affine root systems
1992
Earlier work this paper cites.
I. Cherednik: Double affine Hecke algebras, Knizhnik–Zamolodchikov equations, and Macdonald’s operators
1992
Earlier work this paper cites.
T. H. Koornwinder: Askey-Wilson polynomials for root systems of type B C BC
1992
Earlier work this paper cites.
A. P. Polychronakos: Exchange operator formalism for integrable systems of particles
1992
Earlier work this paper cites.
Y. Shibukawa, K. Ueno: Completely ℤ \mathbb{Z} symmetric R R matrix
1992
Earlier work this paper cites.
H. Ujino, K. Hikami, M. Wadati: Integrability of the quantum Calogero-Moser model
1992
Earlier work this paper cites.
D. Bernard, M. Gaudin, F. D. M. Haldane, V. Pasquier: Yang–Baxter equation in spin chains with long range interactions
1993
Earlier work this paper cites.
E. M. Opdam: Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group
1993
Cited alongside, same era.
B. S. Shastry, B. Sutherland: Super Lax pairs and infinite symmetries in the 1 / r 2 1/r^{2} system
1993
Cited alongside, same era.
V. Buchstaber, G. Felder, A. Veselov: Elliptic Dunkl operators, root systems, and functional equations
1994
Cited alongside, same era.
J. F. van Diejen: Integrability of difference Calogero–Moser systems
1994
Cited alongside, same era.
I. Cherednik: Elliptic quantum many-body problem and double affine Knizhnik–Zamolodchikov equation
1995
Cited alongside, same era.
I. Cherednik: Difference-elliptic operators and root systems
1995
P. Etingof, V. Ginzburg: Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphism
2002
Later among the works it cites.
I. Krichever: Vector bundles and Lax equations on algebraic curves
2002
Later among the works it cites.
C. F. Dunkl, E. M. Opdam: Dunkl operators for complex reflection groups
2003
Later among the works it cites.
I. G. Macdonald. Affine Hecke algebras and orthogonal polynomials. CUP, Cambridge 2003
2003
Later among the works it cites.
A. Oblomkov: Double affine Hecke algebras and Calogero–Moser spaces
2004
Later among the works it cites.
A. N. Sergeev, A. P. Veselov: Deformed quantum Calogero-Moser problems and Lie superalgebras
2004
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
A. Gorsky, N. Nekrasov: Relativistic Calogero-Moser model as gauged WZW theory
1995
Cited alongside, same era.
I. Krichever, A. Zabrodin: Spin generalization of the Ruijsenaars–Schneider model, the nonabelian two-dimensionalized Toda lattice, and representations of the Sklyanin algebra
1995
Cited alongside, same era.
M. Noumi: Macdonald–Koornwinder polynomials and affine Hecke rings
1995
Cited alongside, same era.
J. F. van Diejen: Commuting difference operators with polynomial eigenfunctions
1995
Cited alongside, same era.
N. Nekrasov: Holomorphic bundles and many-body systems
1996
Cited alongside, same era.
K. Hasegawa: Ruijsenaars Commuting Difference Operators as Commuting Transfer Matrices
1997
Cited alongside, same era.
I. Cherednik. Double Affine Hecke Algebras. LMS Lecture Note Ser. 319
2005
Later among the works it cites.
P. Etingof: Calogero–Moser systems and representation theory
2007
Later among the works it cites.
L. Fehér, B. G. Pusztai: A class of Calogero type reductions of free motion on a simple Lie group
2007
Later among the works it cites.
I. Krichever, O. Sheinman: Lax operator algebras
2007
Later among the works it cites.
D. Ben-Zvi, T. Nevins: From solitons to many-body systems
2008
Later among the works it cites.
P. Etingof, X. Ma: On elliptic Dunkl operators
2008
Later among the works it cites.
G. Letzter, J. Stokman: Macdonald difference operators and Harish-Chandra series
2008
Later among the works it cites.
J. F. van Diejen, M. Ito: Difference equations and Pieri formulas for G 2 G_{2} type Macdonald polynomials and integrability
2008
Later among the works it cites.
L. Fehér, C. Klimcík: Poisson-Lie generalization of the Kazhdan–Kostant–Sternberg reduction
2009
Later among the works it cites.
A. N. Sergeev, A. P. Veselov: Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials
2009
Later among the works it cites.
P. Etingof, G. Felder, X. Ma, A. Veselov: On elliptic Calogero–Moser systems for complex crystallographic reflection groups
2011
Later among the works it cites.
J. F. van Diejen, E. Emsiz: A generalized Macdonald operator
2011
Later among the works it cites.
M. Feigin: Generalized Calogero-Moser systems from rational Cherednik algebras
2012
Later among the works it cites.
A. M. Levin, M. A. Olshanetsky, A. V. Smirnov, A. V. Zotov: Calogero–Moser systems for simple Lie groups and characteristic classes of bundles
2012
Later among the works it cites.
B. G. Pusztai: The hyperbolic B C n BC_{n} Sutherland and the rational B C n BC_{n} Ruijsenaars–-Schneider-–van Diejen models: Lax matrices and duality
2012
Later among the works it cites.
E. Rains, S. Ruijsenaars: Difference operators of Sklyanin and van Diejen type
2013
Later among the works it cites.
M. Feigin, A. Silantyev: Generalized Macdonald-Ruijsenaars systems
2014
Later among the works it cites.
A. N. Sergeev, A. P. Veselov: Dunkl operators at infinity and Calogero–Moser systems
2015
Later among the works it cites.
O. Chalykh, A. Silantyev: KP hierarchy for the cyclic quiver
2017
Later among the works it cites.
T. Görbe, B. G. Pusztai: Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters
2017
Later among the works it cites.