Fuchsian differential equations of order 3 and 6 with three singular points and with one accessory parameter

Masaaki Yoshida (Fukuoka U)

Oct 15. 2024, 15:30 — 16:45

A most naive generalization of the Gauss hypergeometric equation would be an equation $H_3$ of order three with three singular points, which has one accessory parameter.

An `addition and middle convolution' takes $H_3$ to an equation $H_6$ of order six  with three singular points and one accessory parameter.

We study shift operators and symmetry of $H_6$ and get a restriction $E_6$ of $H_6$, where the accessory parameter is a cubic polynomials of the local exponents.

An `addition and middle convolution' takes $E_6$ to a restriction $E_3$ of $H_3$. The Dotsenko-Fateev $SE_3$ equation is a special case of $E_3$.

We study shift operators and special solutions of $SE_3$.

 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Algebraicity and Transcendence for Singular Differential Equations (Workshop)
Organizer(s):
Alin Bostan (INRIA Paris)
Francis Brown (U Oxford)
Herwig Hauser (U of Vienna)
Shihoko Ishii (U Tokyo)
Hiraku Kawanoue (Chubu U, Kasugai City)
Michael Singer (NC State U, Raleigh)