Identyfikatory
URI
http://dx.doi.Org/10.7494/OpMath.2015.35.5.665
Warianty tytułu
Języki publikacji
Abstrakty
We give a concrete relation between Katz's middle convolution and Yokoyama's extension and show the equivalence of both algorithms using these operations for the reduction of Fuchsian systems on the Riemann sphere.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
665--688
Opis fizyczny
Bibliogr. 16 poz., tab.
Twórcy
autor
- Josai University Faculty of Science 2-3-20, Hirakawacho, Chiyodaku, Tokyo 102-0093, Japan
Bibliografia
- [1] W. Crawley-Boevey, On matrices in prescribed conjugacy classes with no common invariant sub spaces and sum zero, Duke Math. J. 118 (2003), 339-352.
- [2] M. Dettweiler, S. Reiter, An algorithm of Katz and its applications to the inverse Galois problems, J. Symbolic Comput. 30 (2000), 761-798.
- [3] M. Dettweiler, S. Reiter, Middle convolution of Fuchsian systems and the construction of rigid differential systems, J. Algebra 318 (2007), 1-24.
- [4] Y. Haraoka, Integral representations of solutions of differential equations free from accessory parameters, Adv. Math. 169 (2002), 187-240.
- [5] Y. Haraoka, G. M. Filipuk, Middle convolution and deformation for Fuchsian systems, J. Lond. Math. Soc. 76 (2007), 438-450.
- [6] Y. Haraoka, T. Yokoyama, Construction of rigid local systems and integral representations of their sections, Math. Nachr. 279 (2006), 255-271.
- [7] V.C. Kac, Infinite Dimensional Lie Algebras, 3rd ed., Cambridge Univ. Press, 1990.
- [8] H.M. Katz, Rigid Local Systems, Annals ol Mathematics Studies 139, Princeton University Press, 1995.
- [9] M. Kohno, Global Analysis in Linear Differential Equations, Kluwer Academic Publishers, 1999.
- [10] V.P. Rostov, On the Deligne-Simpson problem, Trudy Mat. Inst. Steklov. 238 (2001), 158-195.
- [11] V.P. Rostov, The Deligne-Simpson problem for zero index of rigidity, Perspective in Complex Analysis, Differential Geometry and Mathematical Physics, World Scientific 2001, 1-35.
- [12] V.P. Rostov, The Deligne-Simpson problem - a survey, J. Algebra 281 (2004), 83-108.
- [13] T. Oshima, A quantization of conjugacy classes of matrices, Advances in Math. 196 (2005), 124-146.
- [14] T. Oshima, Classification of Fuchsian systems and their connection problem, RIMS Rokyuroku Bessatsu B37 (2013), 163-192.
- [15] T. Oshima, Fractional calculus of Weyl algebra and Fuchsian differential equations, MSJ Memoirs 28, Mathematical Society of Japan, 2013.
- [16] T. Yokoyama, Construction of systems of differential equations of Okubo normal form with rigid monodromy, Math. Nachr. 279 (2006), 327-348.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-794dc472-de57-4337-86d6-e66fa67dfcc5