Equilibria of 'discrete' integrable systems and deformation of classical orthogonal polynomials

Journal of Physics A: Mathematical and General

Volumn 37, Issue 49, 2004, Pages 11841-11876

  Odake, S ^a   Sasaki, R ^b  

^a SHINSHU UNIVERSITY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10244231888     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/49/006     Document Type: Article

References (31)

1. Calogero F 1971 Solution of the one-dimensional N-body problem with quadratic and/or inversely quadratic pair potentials J. Math. Phys. 12 419
2. Sutherland B 1972 Exact results for a quantum many-body problem in one-dimension. II Phys. Rev. A 5 1372-6
3. 2ax Lett. Nuovo Cimento 13 383-7 Calogero F 1975 Exactly solvable one-dimensional many body problems Lett. Nuovo Cimento 13 411-6
4. 2ax Lett. Nuovo Cimento 13 383-7 Calogero F 1975 Exactly solvable one-dimensional many body problems Lett. Nuovo Cimento 13 411-6
5. 2ax Lett. Nuovo Cimento 13 383-7 Calogero F 1975 Exactly solvable one-dimensional many body problems Lett. Nuovo Cimento 13 411-6
6. 2ax Lett. Nuovo Cimento 13 383-7 Calogero F 1975 Exactly solvable one-dimensional many body problems Lett. Nuovo Cimento 13 411-6
7. Corrigan E and Sasaki R 2002 Quantum vs classical integrability in Calogero-Moser systems J. Phys. A: Math. Gen. 35 7017-62
8. Ragnisco O and Sasaki R 2004 Quantum vs classical integrability in Ruijsenaars-Schneider systems J. Phys. A: Math. Gen. 37 469-79 Sasaki R 2003 Quantum vs classical integrability in Ruijsenaars-Schneider and Calogero-Moser systems Czech. J. Phys. 53 1111-8
9. Ragnisco O and Sasaki R 2004 Quantum vs classical integrability in Ruijsenaars-Schneider systems J. Phys. A: Math. Gen. 37 469-79 Sasaki R 2003 Quantum vs classical integrability in Ruijsenaars-Schneider and Calogero-Moser systems Czech. J. Phys. 53 1111-8
10. M Ruijsenaars S N and Schneider H 1986 A new class of integrable systems and its relation to solitons Ann. Phys. 170 370-405 M Ruijsenaars S N 1987 Complete integrability of relativistic Calogero-Moser systems and elliptic function identities Commun. Math. Phys. 110 191-213
11. M Ruijsenaars S N and Schneider H 1986 A new class of integrable systems and its relation to solitons Ann. Phys. 170 370-405 M Ruijsenaars S N 1987 Complete integrability of relativistic Calogero-Moser systems and elliptic function identities Commun. Math. Phys. 110 191-213
12. van Diejen J F 1995 The relativistic Calogero model in an external field Preprint solv-int/9509002 van Diejen J F 1995 Multivariable continuous Hahn and Wilson polynomials related to integrable difference systems J. Phys. A: Math. Gen. 28 L369-74
13. van Diejen J F 1995 The relativistic Calogero model in an external field Preprint solv-int/9509002 van Diejen J F 1995 Multivariable continuous Hahn and Wilson polynomials related to integrable difference systems J. Phys. A: Math. Gen. 28 L369-74
14. van Diejen J F 1995 Difference Calogero-Moser systems and finite Toda chains J. Math. Phys. 36 1299-323
15. van Diejen J F 1994 Integrability of difference Calogero-Moser systems J. Math. Phys. 35 2983-3004
16. Calogero F 1977 On the zeros of the classical polynomials Lett. Nuovo Cimenta 19 505-7 Calogero F 1977 Equilibrium configuration of one-dimensional many-body problems with quadratic and inverse quadratic pair potentials Lett. Nuovo Cimenta 22 251-3
17. Calogero F 1977 On the zeros of the classical polynomials Lett. Nuovo Cimenta 19 505-7 Calogero F 1977 Equilibrium configuration of one-dimensional many-body problems with quadratic and inverse quadratic pair potentials Lett. Nuovo Cimenta 22 251-3
18. Odake S and Sasaki R 2002 Polynomials associated with equilibrium positions in Calogero-Moser systems J. Phys. A: Math. Gen. 35 8283-314
19. N algebra Nucl. Phys. B 449 347-74
20. N algebra Nucl. Phys. B 449 347-74
21. Stanley R P 1989 Some combinatorial properties of Jack symmetric functions Adv. Math. 77 76-115
22. N algebras and Macdonald polynomials Commun. Math. Phys. 179 401-16
23. N algebras and Macdonald polynomials Commun. Math. Phys. 179 401-16
24. Andrews G E, Askey R and Roy R 1999 Special functions Encyclopedia of Mathematics and its Applications (Cambridge: Cambridge University Press)
25. Koekoek R and Swarttouw R F 1996 The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Preprint math.CA/9602214
26. Bordner A J, Manton N S and Sasaki R 2000 Calogero-Moser models V: supersymmetry and quantum lax pair Prog. Theor. Phys. 103 463-87 Khastgir S P, Pocklington A J and Sasaki R 2000 Quantum Calogero-Moser models: integrability for all root systems J. Phys. A: Math. Gen. 33 9033-64
27. Bordner A J, Manton N S and Sasaki R 2000 Calogero-Moser models V: supersymmetry and quantum lax pair Prog. Theor. Phys. 103 463-87 Khastgir S P, Pocklington A J and Sasaki R 2000 Quantum Calogero-Moser models: integrability for all root systems J. Phys. A: Math. Gen. 33 9033-64
28. Szegö G 1939 Orthogonal polynomials Am. Math. Soc. New York
29. Macdonald I G 1995 Symmetric Functions and Hall Polynomials 2nd edn (Oxford: Oxford University Press)
30. Chihara T S 1978 An Introduction to Orthogonal Polynomials (New York: Gordon and Breach)
31. Jing S and Yang W 2002 A new kind of deformed Hermite polynomials and its application Preprint math-ph/0212011