The Lie Group Structure of Genus Two Hyperelliptic ℘ Functions



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Submitted May 1, 2023
Published Jun 26, 2023
10.24018/ejmath.2023.4.3.244

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We consider the generalized dual transformation for hyperelliptic ℘ functions. For the genus two case, by constructing a quadratic invariant form, we find that hyperelliptic ℘ functions have the SO(3,2) ∼= Sp(4,R)/Z2 Lie group structure.

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Keywords: generalized dual transformation Genus two hyperelliptic ℘ function SO(3,2) ∼= Sp(4,R)/Z2 Lie group structure Higher dimensional KdV equation

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