On \(F\)-data of automorphism groups of compact Riemann surfaces. The case of \(A_ 5\)
Let \(X\) be a compact Riemann surface of genus \(g\geq 2\) and let \(\Aut(X)\) be the conformal automorphism group on \(X\). Since an automorphism induces a linear transformation of the space of holomorphic differentials on \(X\), there is a canonical representation \(\rho\) of \(\Aut(X)\to GL(g,\mathbb{C})\). In this paper, the author studies conditions for a subgroup \(A_ 5\) of \(GL(g,\mathbb{C})\) satisfying \(CY\)- and \(RH\)-conditions [for the definition, refer \textit{I. Kuribayashi}, Kodai Math. J. 7, 222-237 (1984; Zbl 0575.32025)] to be conjugate to the image under \(\rho\) of a subgroup of \(\Aut(X)\). To state these conditions, the author introduce a collection of nonnegative integers (which he called \(F\)-data in the title), inducing from characters of \(\rho\) and the fixed points of a subgroup of \(\Aut(X)\).
scientific article; zbMATH DE number 60675