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A \(\text{SL}(2)\) covariant theory of genus 2 hyperelliptic functions. (English) Zbl 1063.33001

In this note the authors consider the family of genus two plane curves \[ y^2=\lambda_6x^6+\lambda_5x^5+\lambda_4x^4+ \lambda_3x^3+\lambda_2x^2+\lambda_1x+\lambda_0. \] They give an algebraic formulation of their functions in terms of \(\text{SL}_2({\mathbb C})\) representations, allowing a simple interpretation of all identities in representation theory terms.

MSC:

14H42 Theta functions and curves; Schottky problem
13A50 Actions of groups on commutative rings; invariant theory
14H45 Special algebraic curves and curves of low genus
14H70 Relationships between algebraic curves and integrable systems
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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