|Speaker:||Toshi Oshima (Graduate School of Mathematical Sciences, University of Tokyo)|
Fractional calculus of Weyl algebra and its application
to ordinary differential equations on the Riemann sphere
|Date (JST):||Tue, Sep 08, 2009, 13:15 - 14:45|
|Place:||Seminar Room at IPMU Prefab. B|
We construct an action of a Kac-Moody Weyl group on the totality
of Fuchsian differential equations and give a universal model of
the equations with a given spectral type. Moreover we obtain
explicit connection coefficients for the rigid Fuchsian differential
equations and give a unified interpretation of confluence, contiguity
relation for ordinary differential equations together with its
generalization to partial differential equations.
The integral representation and series expansion of their solutions
are also within our interpretation.