Algebraic solutions of Irregular Garnier systems

Speaker: Frank Loray, CNRS-IRMAR, Rennes.

Date: 27 mar 2019, 14h.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: We prove that algebraic solutions of Garnier systems in the irregular case are of two types, generalizing a result of Ohyama and Okumura for Painlevé equations (rank N=1). The so called "classical solutions" come from isomonodromic deformations of linear equations with diagonal or dihedral differential Galois group; we give a complete list in the rank N = 2 case (two indeterminates). The "pull-back solutions" come from deformations of coverings over a fixed degenerate hypergeometric equation; we provide a complete list when the differential Galois group is SL2(C).

By the way, we have a complete list of algebraic solutions for the rank N = 2 irregular Garnier systems. The rank N=1 case correspond to Painlevé equations I to V and is classical; it has been revisited from this point of view by Ohyama and Okumura.

This is joint work with Karamoko Diarra (Bamako University, Mali).