We generalize Chevalley's theorem about restriction of \mathfrak{ g}-invariant polynomial functions \mathfrak{ g}->C to W-invariant functions on the Cartan \mathfrak{ h}->C. We consider the case when \mathfrak{ g} is replaced by a quantum group and the target space of the polynomial maps is replaced by a finite dimensional representation V of this quantum group. We prove that the restriction map Res:(O_q(G)\otimes V)^{ U_q(\mathfrak{ g})}-> O(H)\otimes V is injective and describe the image.
Categories: math.QA math.RT