Abstract
We investigate the structure of $\tau$-functions for the elliptic difference Painlevé equation of type $E_8$. Introducing the notion of ORG $\tau$-functions for the $E_8$ lattice, we construct some particular solutions which are expressed in terms of elliptic hypergeometric integrals. Also, we discuss how this construction is related to the framework of lattice $\tau$-functions associated with the configuration of generic nine points in the projective plane.
Information
Published: 1 January 2018
First available in Project Euclid: 21 September 2018
zbMATH: 07039299
Digital Object Identifier: 10.2969/aspm/07610001
Subjects:
Primary:
39A20
Secondary:
33D70
,
33E17
Keywords:
$\tau$-function
,
$E_8$ lattice
,
Casorati determinant
,
elliptic hypergeometric integral
,
elliptic Painlevé equation
,
Hirota equation
Rights: Copyright © 2018 Mathematical Society of Japan
