2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64399We shall give a uniform expression and a uniform calculation for the b-functions of prehomogeneous vector spaces of commutative parabolic type, which were previously calculated by case-by-case analysis. Our method is a generalization of Kashiwara's approach using the universal Verma modules. We shall also give a new proof for the criterion of the irreducibility of the generalized Verma module in terms of b-functions due to Suga, Gyoja, Wachi.20 pages, LaTeX2eRepresentation Theory17B10; 20G05text