2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71893We make precise conjectures relating the genus zero Gromov-Witten theory of a nonabelian GIT quotient X//G to that of the associated abelian quotient X//T by a maximal torus T in G.These conjectures imply in particular closed formulas for the J-functions (that is, the generating functions for 1-point Gromov-Witten invariants) of all generalized flag manifolds of classical A, B, C and D types. These formulas are proved in the second part of the paper.15 pages, no figures, LaTeXAlgebraic Geometry14N35, 14M15text