2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77984We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin^c-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted quantization formula in the presence of commuting Hamiltonian actions. The corresponding Morse-type inequalities in holomorphic situations are also established.17 pagesGeometric Topologytext