Group Actions on Riemann-Roch Space

Abstract

Let $G$ be a group acting on a compact Riemann surface $\mathcal{X}$ and $D$ be a $G$-invariant divisor on $\mathcal{X}.$ The action of $G$ on $\mathcal{X}$ induces a linear representation $L_G(D)$ of $G$ on the Riemann-Roch space associated to $D.$ In this paper we give some results on the decomposition of $L_G(D)$ as sum of complex irreducible representations of $G,$ for $D$ an effective non-special $G$-invariant divisor. In particular, we give explicit formulae for the multiplicity of each complex irreducible factor in $L_G(D)$. We work out some examples on well known families of curves.

Cited by in corpus (1)

• Galois structure of the holomorphic differentials of curves