Bibliography

1

F. V. Andreev and A. V. Kitaev, Transformations ${RS}_4^2(3)$ of the ranks $\leq4$ and algebraic solutions of the sixth Painlevé equation, preprint, nlin.SI/0107074.

2

B. Dubrovin and M. Mazzocco, Monodromy of certain Painleve VI transcendents and reflection groups, Invent. Math. 141 (2000) 55-147.

3

N. J. Hitchin, Poncelet polygons and the Painlevé equations, Geometry and analysis (Bombay, 1992) 151-185, Tata Inst. Fund. Res., Bombay, 1995.

4

K. Iwasaki, H. Kimura, S. Shimomura and M. Yoshida, From Gauss to Painlevé - A Modern Theory of Special Functions, Aspects of Mathematics E16, Vieweg, 1991.

5

K. Kajiwara and T. Masuda, On the Umemura polynomials for the Painlevé III equation, Phys. Lett. A 260 (1999) 462-467.

6

K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta and Y. Yamada, Determinant formulas for the Toda and discrete Toda equations, Funkcial. Ekvac. 44 (2001) 291-307.

7

K. Kajiwara and Y. Ohta, Determinant structure of the rational solutions for the Painlevé II equation, J. Math. Phys. 37 (1996) 4693-4704.

8

K. Kajiwara and Y. Ohta, Determinant structure of the rational solutions for the Painlevé IV equation, J. Phys. A: Math. Gen. 31 (1998) 2431-2446.

9

A. N. Kirillov and M. Taneda, Generalized Umemura polynomials, to appear in Rocky Mountain Journal of Mathematics, math.CO/0010279.

10

A. N. Kirillov and M. Taneda, Generalized Umemura polynomials and Hirota-Miwa equations, to appear in MSJ Memoirs, math.CO/0106025.

11

K. Koike, 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

T. Masuda, Y. Ohta and K. Kajiwara, A determinant formula for a class of rational solutions of Painlevé V equation, to appear in Nagoya Math. J. 168 (2002), nlin.SI/0101056.

13

M. Mazzocco, Picard and Chazy solutions to the Painlevé VI equation, Math. Ann. 321 (2001) 157-195.

14

M. Mazzocco, Rational solutions of the Painlevé VI equation, J. Phys. A: Math. Gen. 34 (2001) 2281-2294.

15

M. Noumi, S. Okada, K. Okamoto, and H. Umemura, 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

M. Noumi and Y. Yamada, Symmetries in the fourth Painlevé equation and Okamoto polynomials, Nagoya Math. J. 153 (1999) 53-86.

17

M. Noumi and Y. Yamada, Umemura polynomials for the Painlevé V equation, Phys. Lett. A247 (1998) 65-69.

18

M. Noumi and Y. Yamada, Higher order Painlevé equations of type $A_l^{(1)}$, Funkcial. Ekvac. 41 (1998) 483-503.

19

M. Noumi and Y. Yamada, Affine Weyl groups, discrete dynamical systems and Painlevé equations, Commun. Math. Phys. 199 (1998) 281-295.

20

M. Noumi and Y. Yamada, A new Lax pair for the sixth Painlevé equation associated with $\widehat{\mathfrak{so}}(8)$, to appear in Microlocal Analysis and Complex Fourier Analysis, World Scientific, math-ph/0203029.

21

K. Okamoto, Studies on the Painlevé equations I, sixth Painlevé equation P$_{\rm VI}$, Annali di Matematica pura ed applicata CXLVI (1987) 337-381.

22

K. Okamoto, Studies on the Painlevé equations II, fifth Painlevé equation P$_{\rm V}$, Japan J. Math. 13 (1987) 47-76.

23

K. Okamoto, Studies on the Painlevé equations III, second and fourth Painlevé equations, P$_{\rm II}$ and P$_{\rm IV}$, Math. Ann. 275 (1986) 222-254.

24

K. Okamoto, Studies on the Painlevé equations IV, third Painlevé equation P$_{\rm III}$, Funkcial. Ekvac. 30 (1987) 305-332.

25

P. Painlevé, Sur les équations différentielles du second ordre à points critiques fixes, C. R. Acad. Sci. Paris 143 (1906) 1111-1117.

26

M. Taneda, Polynomials associated with an algebraic solution of the sixth Painlevé equation, to appear in Jap. J. Math. 27 (2002).

27

H. Umemura, Special polynomials associated with the Painlevé equations I, preprint.

28

A. P. Vorob'ev, On rational solutions of the second Painlevé equation. Diff. Uravn. 1 (1965) 58-59.

29

Y. Yamada, Determinant formulas for the $\tau$-functions of the Painlevé equations of type $A$, Nagoya Math. J. 156 (1999) 123-134.