On a Class of Algebraic Solutions to the Painlevé VI Equation, Its Determinant Formula and Coalescence Cascade

Funkcialaj Ekvacioj

Volumn 46, Issue 1, 2003, Pages 121-171

  Masuda, Tetsu ^a  

^a KOBE UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042096875     PISSN: 05328721     EISSN: None     Source Type: Journal    
DOI: 10.1619/fesi.46.121     Document Type: Article

References (29)

1. Andreev, F. V. and Kitaev, A. V., Transformations RS24(3) of the ranks ≤4 and algebraic solutions of the sixth Painlevé equation, Commun. Math. Phys., 228 (2002), 151-176
2. Dubrovin, B. and Mazzocco, M., Monodromy of certain Painleve VI transcendents and reflection groups, Invent. Math., 141 (2000), 55-147
3. Hitchin, N. J., Poncelet polygons and the Painlevé equations, Geometry and analysis (Bombay, 1992) 151-185, Tata Inst. Fund. Res., Bombay, 1995
4. Iwasaki, K., Kimura, H., Shimomura, S. and Yoshida, M., From Gauss to Painlevé—A Modern Theory of Special Functions, Aspects of Mathematics E16, Vieweg, 1991
5. Kajiwara, K. and Masuda, T., On the Umemura polynomials for the Painlevé III equation, Phys. Lett., A 260 (1999), 462-467
6. Kajiwara, K., Masuda, T., Noumi, M., Ohta, Y. and Yamada, Y., Determinant formulas for the Toda and discrete Toda equations, Funkcial. Ekvac., 44 (2001), 291-307
7. Kajiwara, K. and Ohta, Y., Determinant structure of the rational solutions for the Painlevé II equation, J. Math. Phys., 37 (1996), 4693-4704
8. Kajiwara, K. and Ohta, Y., Determinant structure of the rational solutions for the Painlevé IV equation, J. Phys. A: Math. Gen., 31 (1998), 2431-2446
9. Kirillov, A. N. and Taneda, M., Generalized Umemura polynomials, Rocky Mountain J. Math., 32 (2002), 691-702
10. Kirillov, A. N. and Taneda, M., Generalized Umemura polynomials and Hirota-Miwa equation, MathPhys Odyssey, 2001, 313-331, Prog. Math. Phys., 23
11. Koike, K., On the decomposition of tensor products of the representations of the classical groups: by means of the universal characters, Adv. Math., 74 (1989), 57-86
12. Masuda, T., Ohta, Y. and Kajiwara, K., A determinant formula for a class of rational solutions of Painlevé V equation, Nagoya Math. J., 168 (2002), 1-25
13. Mazzocco, M., Picard and Chazy solutions to the Painlevé VI equation, Math. Ann., 321 (2001), 157-195
14. Mazzocco, M., Rational solutions of the Painlevé VI equation, J. Phys. A: Math. Gen., 34 (2001), 2281-2294
15. Noumi, M., Okada, S., Okamoto, K. and Umemura, H., Special polynomials associated with the Painleve equations II, In: Saito, M. H., Shimizu, Y., Ueno, K. (eds.) Proceedings of the Taniguchi Symposium, 1997, Integrable Systems and Algebraic Geometry. Singapore: World Scientific, 1998, pp. 349-372
16. Noumi, M. and Yamada, Y., Symmetries in the fourth Painlevé equation and Okamoto polynomials, Nagoya Math. J., 153 (1999), 53-86
17. Noumi, M. and Yamada, Y., Umemura polynomials for the Painlevé V equation, Phys. Lett., A247 (1998), 65-69
18. Noumi, M. and Yamada, Y., Higher order Painlevé equations of type Al(1), Funkcial. Ekvac., 41 (1998), 483-503
19. Noumi, M. and Yamada, Y., Affine Weyl groups, discrete dynamical systems and Painlevé equations, Commun. Math. Phys., 199 (1998), 281-295
20. Noumi, M. and Yamada, Y., A new Lax pair for the sixth Painlevé equation associated with SO(8), In: Kawai, T., and Fujita, K. (eds.) Microlocal Analysis and Complex Fourier Analysis, World Scientific, 2002, pp. 238-252
21. Okamato, K., Studies on the Painlevé equations I, sixth Painlevé equation PVI, Annali di Matematica pura ed applicata, 146 (1987), 337-381
22. Okamoto, K., Studies on the Painlevé equations II, fifth Painlevé PV, Japan J. Math., 13 (1987), 47-76
23. Okamoto, K., Studies on the Painlevé equations III, second and fourth Painlevé equations, PII and PIV, Math. Ann., 275 (1986), 222-254
24. Okamoto, K., Studies on the Painlevé equations IV, third Painlevé equation PIII, Funkcial. Ekvac., 30 (1987), 305-332
25. Painlevé, P., Sur les équations différentielles du second ordre à points critiques fixes, C. R. Acad. Sci. Paris, 143 (1906), 1111-1117
26. Taneda, M., Polynomials associated with an algebraic solution of the sixth Painlevé equation, Jap. J. Math., 27 (2001), 257-274
27. Umemura, H., Special Polynomials associated with the Painlevé equations I, preprint
28. Vorob'ev, A. P., On rational solutions of the second Painlevé equation, Diff. Uravn., 1 (1965), 58-59
29. Yamada, Y., Determinant formulas for the τ-functions of the Painlevé equations of type A, Nagoya Math. J., 156 (1999), 123-134