Notes on the Elliptic Ruijsenaars Operators

Letters in Mathematical Physics

Volumn 46, Issue 2, 1998, Pages 147-155

  Komori, Yasushi ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Lam operators; Ruijsenaars operators; Yang Baxter equation

Indexed keywords

EID: 0000909069     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007577231399     Document Type: Article

References (25)

1. Bourbaki, N.: Groupes et algèbre de Lie, Hermann, Paris, 1969.
2. Cherednik, I.: Factorizing particles on a half-line and root systems, Theor. Math. Phys. 61 (1984), 35-44.
3. Cherednik, I.: Double affine Hecke algebras, Knizhnik-Zamolodchikov equations, and Macdonald's operators, Internat. Math. Res. Notices 9 (1992), 171-180.
4. Cherednik, I.: Quantum Knizhnik-Zamolodchikov equations and affine root systems, Comm. Math. Phys. 150 (1992), 109-136.
5. Cherednik, I.: Difference-elliptic operators and root systems, Internat. Math. Res. Notices 1 (1995a), 43-59.
6. Cherednik, I.: Elliptic quantum many-body problem and double affine Knizhnik-Zamolodchikov equation, Comm. Math. Phys. 169 (1995b), 441-461.
7. Gaudin, M.: Matrices R de dimension infinie, J. Phys. France 49 (1988), 1857-1865.
8. Hasegawa, K.: Ruijsenaars' commuting difference operators as commuting transfer matrices, Comm. Math. Phys. (1997), 289-325.
9. Humphreys, J. E.: Reflection Groups and Coxeter Groups, Cambridge Univ. Press, Cambridge, 1990.
10. Hurwitz, A. and R. Courant: Vorlesungen über Allgemeine Funktionentheorie und Elliptische Funktionen, Springer-Verlag, Berlin, 1964.
11. Komori, Y. and K. Hikami, Conserved operators of the generalized elliptic Ruijsenaars models, J Math. Phys. to appear.
12. Komori, Y. and K. Hikami: Elliptic K-matrix associated with Belavin's symmetric R-matrix, Nuclear Phys. B 494 (1997), 687-701.
13. Komori, Y. and K. Hikami: Quantum integrability of the generalized elliptic Ruijsenaars models, J. Phys. A 30 (1997), 4341-4364.
14. Komori, Y. and K. Hikami: Affine R-matrix and the generalized elliptic Ruijsenaars models, Lett. Math. Phys. 43 (1998), 335-346.
15. Koornwinder, T. H.: Askey-Wilson polynomials for root systems of type BC, Contemp. Math. 138 (1992), 189-204.
16. Macdonald, I. G.: Symmetric Functions and Hall Polynomials, 2nd edn, Oxford Univ. Press, Oxford, 1995.
17. Reed, M. and B. Simon: Fourier Analysis and Self-Adjointness, Vol. II of Methods of Modern Mathematical Physics, Academic Press, New York, 1975.
18. Reed, M. and B. Simon: Functional Analysis, Vol. I of Methods of Modern Mathematical Physics, revised edn, Academic Press, New York, 1980.
19. Ruijsenaars, S. N. M.: Complete integrability of relativistic Calogero-Moser systems and elliptic function identities, Comm. Math. Phys. 110 (1987), 191-213.
20. Ruijsenaars, S. N. M.: Generalized Lamé functions, Preprint, 1997.
21. Shibukawa, Y. and K. Ueno: Completely ℤ symmetric R matrix, Lett. Math. Phys. 25 (1992), 239-248.
22. Sklyanin, E. K.: Boundary conditions for integrable quantum systems, J. Phys. A 21 (1988), 2375-2389.
23. van Diejen, J. F.: Integrability of difference Calogero-Moser systems, J. Math. Phys. 35 (1994), 2983-2998.
24. van Diejen, J. F.: Difference Calogero-Moser systems and finite Toda chains, J. Math. Phys. 36 (1995), 1299-1323.
25. Whittaker, E. T. and G. N. Watson: A Course of Modern Analysis, 4th edn, Cambridge Univ. Press, Cambridge, 1927.