  This article describes a {\em nonstandard} quantum group that may be used to
derive a positive formula for the plethysm problem, just as the standard
(Drinfeld-Jimbo) quantum group can be used to derive the positive
Littlewood-Richardson rule for arbitrary complex semisimple Lie groups. The
sequel \cite{GCT8} gives conjecturally correct algorithms to construct
canonical bases of the coordinate rings of these nonstandard quantum groups and
canonical bases of the dually paired nonstandard deformations of the symmetric
group algebra. A positive $#P$-formula for the plethysm constant follows from
the conjectural properties of these canonical bases and the duality and
reciprocity conjectures herein.
