Covariant Hyperelliptic Functions of Genus Two

We report results of investigations concerning the role of representations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$SL_2 \left( \mathbb{C} \right)$$ \end{document} in the theory of genus-two hyperelliptic functions. We discuss the role of these representations in the classical theory as well as introduce a family of new, naturally covariant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{P}$$ \end{document} functions.