Quantum integrability of the deformed elliptic Calogero–Moser problem

L. A. Khodarinova

Type: Article

Publication Date: 2005-02-10

Citations: 7

DOI: https://doi.org/10.1063/1.1829375

Abstract

The integrability of the deformed quantum elliptic Calogero–Moser problem introduced by Chalykh, Feigin, and Veselov is proven. Explicit recursive formulas for the integrals are found. For integer values of the parameter this implies the algebraic integrability of the systems.

Locations

Journal of Mathematical Physics - View
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	On algebraic integrability of the deformed elliptic Calogero-Moser problem	2004	L. A. Khodarinova I. A. Prikhodsky
+ PDF Chat	On Algebraic Integrability of the Deformed Elliptic CalogeroMoser Problem	2001	L. A. Khodarinova I.A. Prikhodski
+	New integrable generalizations of Calogero–Moser quantum problem	1998	Oleg Chalykh Misha Feigin А. П. Веселов
+ PDF Chat	Algebraic Spectral Relations for Elliptic Quantum Calogero-Moser Problems	1999	L. A. Khodarinova I. A. Prikhodsky
+ PDF Chat	Deformed Quantum Calogero-Moser Problems and Lie Superalgebras	2004	A. N. Sergeev А. П. Веселов
+	Integrability and algebraic structure of the quantum Calogero-Moser model	1993	Miki Wadati Kazuhiro Hikami Hideaki Ujino
+	Dynamics of the Calogero?Moser system and the reduction of hyperelliptic integrals to elliptic integrals	1986	A. R. Its V. Z. �nol'skii
+	Quantum vs. Classical Integrability in Ruijsenaars–Schneider and Calogero–Moser Systems	2003	Ryu Sasaki
+	Direct proof of integrability of Calogero–Moser model	1998	Cezary Gonera
+	New integrable deformations of the Calogero-Moser quantum problem	1996	А. П. Веселов Misha Feigin Oleg Chalykh
+ PDF Chat	Complete integrability of relativistic Calogero-Moser systems and elliptic function identities	1987	S. N. M. Ruijsenaars
+ PDF Chat	Integrability of difference Calogero–Moser systems	1994	J. F. van Diejen
+	Additional integrals of the generalized quantum Calogero-Moser problem	1996	Oleg Chalykh
+	On the integrability of the Calogero-Moser system in an external quartic potential and other many-body systems	1984	S. Wojciechowski
+	Algebraic spectral relations for elliptic quantum Calogero-Moser problems	2004	L. A. Khodarinova I. A. Prikhodsky
+ PDF Chat	Hidden symmetry of the quantum Calogero-Moser system	1996	В. Б. Кузнецов
+ PDF Chat	Degenerate integrability of quantum spin Calogero–Moser systems	2016	Nicolai Reshetikhin
+	Additional Constants of Motion for a Discretization of the Calogero–Moser Model	2008	Hideaki Ujino Luc Vinet Tetsu Yajima Haruo Yoshida
+	Integrability of Calogero-Moser Spin System	1993	Kazuhiro Hikami Miki Wadati
+ PDF Chat	Liouville integrability of classical Calogero–Moser models	2001	S. Pratik Khastgir Ryu Sasaki

Works That Cite This (7)

Action	Title	Year	Authors
+ PDF Chat	Generalized Calogero–Moser systems from rational Cherednik algebras	2011	Misha Feigin
+ PDF Chat	Deformed Calogero-Sutherland model and fractional quantum Hall effect	2017	Farrokh Atai Edwin Langmann
+	Algebraic integrability of ${\cal PT}$-deformed Calogero models	2021	Francisco Correa Olaf Lechtenfeld
+ PDF Chat	Source Identity and Kernel Functions for Elliptic Calogero–Sutherland Type Systems	2010	Edwin Langmann
+	Algebraic integrability of PT -deformed Calogero models	2021	Francisco Correa Olaf Lechtenfeld
+ PDF Chat	Exact solutions by integrals of the non-stationary elliptic Calogero–Sutherland equation	2020	Farrokh Atai Edwin Langmann
+	A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009	2015	Nelson H. F. Beebe

Works Cited by This (11)

Action	Title	Year	Authors
+ PDF Chat	Generalized Lam� Operators	2003	Oleg Chalykh Pavel Etingof Alexei Oblomkov
+	The congruences of Clausen — von Staudt and Kummer for Bernoulli-Hurwitz numbers	1975	Nicholas M. Katz
+	Quantum completely integrable systems connected with semi-simple Lie algebras	1977	M. A. Olshanetsky A. M. Perelomov
+ PDF Chat	Deformed Quantum Calogero-Moser Problems and Lie Superalgebras	2004	A. N. Sergeev А. П. Веселов
+ PDF Chat	Commuting families of symmetric differential operators	1994	Hiroyuki Ochiai Toshio Oshima Hideko Sekiguchi
+	New integrable generalizations of Calogero–Moser quantum problem	1998	Oleg Chalykh Misha Feigin А. П. Веселов
+	Quantum integrable systems related to lie algebras	1983	M. A. Olshanetsky A. M. Perelomov
+	Commuting families of differential operators invariant under the action of a Weyl group	1995	Toshio Oshima Hideko Sekiguchi
+ PDF Chat	On Algebraic Integrability of the Deformed Elliptic CalogeroMoser Problem	2001	L. A. Khodarinova I.A. Prikhodski
+	A Course of Modern Analysis	1996	E. T. Whittaker G. N. Watson