New integrable generalizations of Calogero-Moser quantum problem

Journal of Mathematical Physics

Volumn 39, Issue 2, 1998, Pages 695-703

  Chalykh, O ^a   Feigin, M ^a   Veselov, A ^b,c  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^c LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032353158     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532347     Document Type: Article

References (18)

1. F. Calogero, "Solution of the one-dimensional n-body problem with quadratic and/or inversely quadratic pair potential," J. Math. Phys. 12, 419-436 (1971).
2. O. A. Chalykh and A. P. Veselov, "Commutative rings of partial differential operators and Lie alrebras," Commun. Math. Phys. 126, 597-611 (1990).
3. I. M. Krichever, "Methods of algebraic geometry in the theory of nonlinear equations," Russ. Math. Surveys 32, 180-208 (1977).
4. A. P. Veselov, K. L. Styrkas, and O. A. Chalykh, "Algebraic integrability for Schrodinger equation and finite reflection groups," Theor. Math. Phys. 94, 253-275 (1993).
5. B. Sutherland, "Exact results for a quantum many-body problem in one dimension," Phys. Rev. A 4, 1372-1390 (1971).
6. M. A. Olshanetsky and A. M. Perelomov, "Quantum integrable systems related to Lie algebras," Phys. Rep. 94, 313-404 (1983).
7. M. Schmidt and A. Veselov, "Elliptic Calogero-Moser quantum problem and deformations of algebraic surfaces," preprint of TU, Berlin (1996).
8. L. Khodarinova "On quantum elliptic Calogero-Moser problem," Vestnik MGU (to be published).
9. G. Felder and A. Varchenko, "Integral representations of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equation," Int. Math. Res. Notices 5, 221-233 (1995).
10. G. Felder and A. Varchenko, "Three formulas for eigenfunctions of integrable Schrödinger operators," preprint of UNC (1995).
11. A. Braverman, P. Etingof, and D. Gaitsgory "Quantum integrable systems and differential Galois theory," preprint (1996).
12. A. P. Veselov, M. V. Feigin, and O. A. Chalykh, "New integrable deformations of quantum Calogero-Moser problem," Usp. Mat. Nauk 51, 185-186 (1996).
13. 2ax," Lett. Nuovo Cimento 13, 383-387 (1975).
14. O. A. Chalykh and A. P. Veselov, "Integrability in the theory of Schrodinger operator and harmonic analysis," Commun. Math. Phys. 152, 29-40 (1993).
15. O. A. Chalykh, "Additional integrals for the generalized Calogero-Moser quantum problem," Teor. Mat. Fiz. 109, 28-33 (1996).
16. Yu. Yu. Berest and A. P. Veselov, "Hadamard's problem and Coxeter groups: new examples of Huygens' equation," Funct. Anal. Appl. 28, 3-15 (1994).
17. S. N. M. Ruijsenaars, "Systems of Calogero-Moser type," in Proceedings of the 1994 Banff summer school 'Particles and fields', edited by G. Semenoff and L.Vinet (to be published).
18. O. A. Chalykh, M. V. Feigin, and A. P. Veselov, "Multidimensional Baker-Akhiezer functions and Huygens' Principle," (unpublished).