Decomposing representations of finite groups on Riemann-Roch spaces

Abstract

If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then we compute a simplified formula for the trace of the natural representation of G on the Riemann-Roch space L(D), under the assumption that L(D) is rational, D is nonspecial, and the characteristic is good. We discuss the partial formulas that result if L(D) is not rational.