Resolving singularities and monodromy reduction of Fuchsian connections
| Autor: | Chin-Yin Tsang, Avery Ching, Yik-Man Chiang |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Nuclear and High Energy Physics
Pure mathematics Reduction (recursion theory) 010102 general mathematics Connection (vector bundle) Statistical and Nonlinear Physics 01 natural sciences Hypergeometric distribution 34M35 14F05 (primary) 33E10 33E17 (secondary) Singularity Monodromy Mathematics - Classical Analysis and ODEs 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics Gravitational singularity 010307 mathematical physics 0101 mathematics Invariant (mathematics) Mathematical Physics Eigenvalues and eigenvectors Mathematics |
| DOI: | 10.48550/arxiv.2009.02871 |
| Popis: | We study monodromy reduction of Fuchsian connections from a sheave theoretic viewpoint, focusing on the case when a singularity of a special connection with four singularities has been resolved. The main tool of study is {based on} a bundle modification technique due to Drinfeld and Oblezin. This approach via invariant spaces and eigenvalue problems allows us not only to explain Erd\'elyi's classical infinite hypergeometric expansions of solutions to Heun equations, but also to obtain new expansions not found in his papers. As a consequence, a geometric proof of Takemura's eigenvalues inclusion theorem is obtained. Finally, we observe a precise matching between the monodromy reduction criteria giving those special solutions of Heun equations and that giving classical solutions of the Painlev\'e VI equation. Comment: Revised after submission. Accepted by Ann Henri Poincar\'e (A Journal of Theoretical and Mathematical Physics) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|