Resolving Singularities and Monodromy Reduction of Fuchsian Connections

被引:0
作者
Chiang, Yik-Man [1 ]
Ching, Avery [1 ]
Tsang, Chiu-Yin [2 ]
机构
[1] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China
[2] Univ Hong Kong, Dept Math, Pokfulam Rd, Hong Kong, Peoples R China
来源
ANNALES HENRI POINCARE | 2021年 / 22卷 / 09期
关键词
DIFFERENTIAL-EQUATIONS; ISOMONODROMIC DEFORMATIONS; POLYNOMIALS; SYSTEMS;
D O I
10.1007/s00023-021-01049-w
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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 Erdelyi'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 Painleve VI equation.
引用
收藏
页码:3051 / 3094
页数:44
相关论文
共 43 条
[1]  
[Anonymous], 1999, CRM Ser. Math. Phys., DOI DOI 10.1007/978-1-4612-1532-52
[2]  
[Anonymous], 1944, The Quarterly Journal of Mathematics
[3]   Removing Apparent Singularities of Systems of Linear Differential Equations with Rational Function Coefficients [J].
Barkatou, Moulay A. ;
Maddah, Suzy S. .
PROCEEDINGS OF THE 2015 ACM ON INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC'15), 2015, :53-60
[4]  
Beukers F, 2007, PROG MATH, V260, P23
[5]   Root asymptotics of spectral polynomials for the Lame operator [J].
Borcea, Julius ;
Shapiro, Boris .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 282 (02) :323-337
[6]   Apparent singularities of D-finite systems [J].
Chen, Shaoshi ;
Kauers, Manuel ;
Li, Ziming ;
Zhang, Yi .
JOURNAL OF SYMBOLIC COMPUTATION, 2019, 95 :217-237
[7]  
Chiang YM., 2018, KUMAMOTO J MATH, V31, P15
[8]  
Chudnovsky D. V., 1989, P S PURE MATH, V49, P167, DOI 10.1090/pspum/049.2/1013173
[9]   The solution of a class of free boundary problems [J].
Craster, RV .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1997, 453 (1958) :607-630
[10]   Applications of Fuchsian differential equations to free boundary problems [J].
Craster, RV ;
Hoang, VH .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1998, 454 (1972) :1241-1252