Toda systems and hypergeometric equations
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- by Chang-Shou Lin, Zhaohu Nie and Juncheng Wei PDF
- Trans. Amer. Math. Soc. 370 (2018), 7605-7626 Request permission
Abstract:
This paper establishes certain existence and classification results for solutions to $\mathrm {SU}(n)$ Toda systems with three singular sources at 0, 1, and $\infty$. First, we determine the necessary conditions for such an $\mathrm {SU}(n)$ Toda system to be related to an $n$th order hypergeometric equation. Then, we construct solutions for $\mathrm {SU}(n)$ Toda systems that satisfy the necessary conditions and also the interlacing conditions from Beukers and Heckman. Finally, for $\mathrm {SU}(3)$ Toda systems satisfying the necessary conditions, we classify, under a natural reality assumption, that all the solutions are related to hypergeometric equations. This proof uses the Pohozaev identity.References
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Additional Information
- Chang-Shou Lin
- Affiliation: Department of Mathematics, Taida Institute of Mathematical Sciences, National Taiwan University, Taipei 106, Taiwan
- MR Author ID: 201592
- Email: cslin@math.ntu.edu.tw
- Zhaohu Nie
- Affiliation: Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322-3900
- MR Author ID: 670293
- Email: zhaohu.nie@usu.edu
- Juncheng Wei
- Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
- MR Author ID: 339847
- ORCID: 0000-0001-5262-477X
- Email: jcwei@math.ubc.ca
- Received by editor(s): October 10, 2016
- Published electronically: August 9, 2018
- Additional Notes: The second author thanks the University of British Columbia, Wuhan University, and the National Taiwan University for hospitality during his visits in 2015 and 2016, where part of this work was done. He also acknowledges the Simons Foundation through Grant #430297.
The research of the third author is partially supported by NSERC of Canada. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 7605-7626
- MSC (2010): Primary 35J47, 33C20
- DOI: https://doi.org/10.1090/tran/7577
- MathSciNet review: 3852442