�@We 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. 
We sketch the proof of these formulas. <BR>
�@This talk is based on joint work 
with Bertram and Ciocan-Fontanine.