2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152197We prove a multiplicity formula for Riemann-Roch numbers of reductions of Hamiltonian actions of loop groups. This includes as a special case the factorization formula for the quantum dimension of the moduli space of flat connections over a Riemann surface.31 pages, AMS-LaTeXDifferential Geometrytext