The half-period addition formulae for genus two hyperelliptic ℘ functions and the Sp(4, ) 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, )/ ≅ SO(3, 2) Lie algebra structure. In this study, by directly using the differential equations of the genus two hyperelliptic ℘ 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, ) Lie group structure.