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arXiv · 1610.03194

Toda systems and hypergeometric equations

Chang-Shou Lin·Zhaohu Nie·Juncheng Wei
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Abstract

This paper establishes certain existence and classification results for solutions to $SU(n)$ Toda systems with three singular sources at 0, 1, and $\infty$. First, we determine the necessary conditions for such an $SU(n)$ Toda system to be related to an $n$th order hypergeometric equation. Then, we construct solutions for $SU(n)$ Toda systems that satisfy the necessary conditions and also the interlacing conditions from Beukers and Heckman. Finally, for $SU(3)$ 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.

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Chang-Shou Lin, Zhaohu Nie, Juncheng Wei. 2016-10-11. Toda systems and hypergeometric equations. https://arxiv.org/abs/1610.03194

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