2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59491We show that there exists a natural q-analogue of the b-function for the prehomogeneous vector space of commutative parabolic type, and calculate them explicitly in each case. Our method of calculating the b-functions seems to be new even for the original case q=1.24 pages, LaTeX2eQuantum Algebra17B37; 17B10; 20G05text