Moduli spaces of d-connections and difference Painleve equations

Abstract

We show that difference Painleve equations can be interpreted as isomorphisms of moduli spaces of d-connections on the projective line with given singularity structure. We also derive a new difference equation. It is the most general difference Painleve equation known so far, and it degenerates to both difference Painleve V and classical (differential) Painleve VI equations.

30 pages (LaTeX)

References in corpus (5)

• Application of the $\tau$-Function Theory of Painlevé Equations to Random Matrices: PIV, PII and the GUE
• Distribution of the first particle in discrete orthogonal polynomial ensembles
• Discrete Painlevé equations and random matrix averages
• Bäcklund Transformations of the Sixth Painlevé Equation in Terms of Riemann-Hilbert Correspondence
• From Discrete to Continuous Painlevé Equations: A Bilinear Approach

Cited by in corpus (1)

• Discrete Schlesinger Transformations, their Hamiltonian Formulation, and Difference Painlevé Equations