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

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.

16 pages

References in corpus (7)

• Multi-Dimensional Sigma-Functions
• The Static Elliptic $N$-soliton Solutions of the KdV Equation
• The Construction of the mKdV Cyclic Symmetric $N$-soliton Solution by the Bäcklund Transformation
• Common Hirota Form Bäcklund Transformation for the Unified Soliton System
• Differential Equations of Genus Four Hyperelliptic $\wp$ Functions
• Elliptic Solutions for Higher Order KdV Equations
• Two Flows Kowalevski Top as the Full Genus Two Jacobi's Inversion Problem and Sp(4,$\mathbb{R}$) Lie Group Structure