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arXiv · 2206.05097

The Half-period Addition Formulae for Genus Two Hyperelliptic $\wp$ Functions and the Sp(4,$\mathbb{R}$) Lie Group Structure

Masahito Hayashi·Kazuyasu Shigemoto·Takuya Tsukioka
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Abstract

In the previous study, by using the two-flows Kowalevski top, we have demonstrated that the genus two hyperelliptic functions provide the Sp(4,$\mathbb{R}$)/$Z_2$ $\cong$ SO(3,2) Lie algebra structure. In this study, by directly using the differential equations of the genus two hyperelliptic $\wp$ functions instead of using integrable models, we demonstrate that the half-period addition formula for the genus two hyperelliptic functions provides the order two Sp(4,$\mathbb{R}$) Lie group structure.

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Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka. 2022-06-10. The Half-period Addition Formulae for Genus Two Hyperelliptic $\wp$ Functions and the Sp(4,$\mathbb{R}$) Lie Group Structure. https://doi.org/10.1088/2399-6528%2Fac8521

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