In this paper we prove that there is only one conjugacy class of
dihedral group of order $2p$ in the $2(p-1)\times 2(p-1)$ integral
symplectic group can be realized by an analytic automorphism
of compact connected Riemann surfaces of genus $p-1$. A pair of
representative generators of the realizable class is also given.
dihedral group, automorphism group, Riemann surface, integral symplectic matrix, fundamental domain
20H25 - Other matrix groups over rings
57M60 - Group actions in low dimensions