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- Title
On the Monodromy Manifold of q-Painlevé VI and Its Riemann–Hilbert Problem.
- Authors
Joshi, Nalini; Roffelsen, Pieter
- Abstract
We study the q-difference sixth Painlevé equation ( q P VI ) through its associated Riemann–Hilbert problem (RHP) and show that the RHP is always solvable for irreducible monodromy data. This enables us to identify the solution space of q P VI with a monodromy manifold for generic parameter values. We deduce this manifold explicitly and show it is a smooth and affine algebraic surface when it does not contain reducible monodromy. Furthermore, we describe the RHP for reducible monodromy data and show that, when solvable, its solution is given explicitly in terms of certain orthogonal polynomials yielding special function solutions of q P VI .
- Subjects
RIEMANN-Hilbert problems; MONODROMY groups; PAINLEVE equations; SPECIAL functions; ORTHOGONAL polynomials; ALGEBRAIC surfaces
- Publication
Communications in Mathematical Physics, 2023, Vol 404, Issue 1, p97
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-023-04834-2