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Języki publikacji
Abstrakty
For monodromy representations of holonomic systems, the rigidity can be defined. We examine the rigidity of the monodromy representations for Appell's hypergeonietric functions, and get the representations explicitly. The results show how the topology of the singular locus and the spectral types of the local monodromies work for the study of the rigidity.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
567--594
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Kumamoto University Department of Mathematics Kumamoto 860-8555, Japan
autor
- Kumamoto High School Shin-Oe 1-8, Kumamoto 862-0972, Japan
Bibliografia
- [1] P. Appell, J. Kampe de Feriet, Fonctions Hypergeometriques et Hyperspheriques - Poly-nomes d'Hermite, Gauthier-Villars et cie, Paris, 1926.
- [2] W.N. Bailey, Generalized Hypergeometric Series, Stechert-Hafner, Inc., New York, 1964.
- [3] R. Gerard, A.H.M. Levelt, Etude d'une classe particuliere de systemes de Pfaff du type de Fuchs sur I'espace projectif complexe, J. Math. Pures Appl. 51 (1972), 189-217.
- [4] Y. Haraoka, Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangements, Adv. Stud. Pure Math. 62 (2012), 109-136.
- [5] Y. Haraoka, T. Matsumura, Monodromy of completely integrable systems of rank 3 singular along free divisors, preprint.
- [6] Y. Haraoka, Y. Ueno, Rigidity for Appell's hypergeometric series Fą,, Funkcial. Ekvac. 51 (2008), 149-164.
- [7] E.R. van Kampen, On the fundamental group of an algebraic curve, Amer. J. Math. 55 (1933), 255-260.
- [8] M. Kato, A Pfaffian system of Appell's FĄ, Bull. College Educ. Univ. Ryukyus 33 (1988), 331-334.
- [9] M. Kato, Connection formulas for Appell's system Fą, and some applications, Funkcial. Ekvac. 38 (1995), 243-266.
- [10] N.M. Katz, Rigid Local Systems, Princeton Univ. Press, Princeton, NJ, 1996.
- [11] T. Kimura, Hype.rgeome.tric Functions of Two Variables, Lecture Notes, Univ. of Minnesota, 1973.
- [12] P. Orlik, H. Terao, Arrangements of Hyperplanes, Springer-Verlag, Berlin, 1992.
- [13] R. Randell, The fundamental group of the complement of a union of complex hyperplanes, Invent. Math. 69 (1982), 103-108.
- [14] G.N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, 1922.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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