  This article gives conjecturally correct algorithms to construct canonical
bases of the irreducible polynomial representations and the matrix coordinate
rings of the nonstandard quantum groups in GCT4 and GCT7, and canonical bases
of the dually paired nonstandard deformations of the symmetric group algebra
therein. These are generalizations of the canonical bases of the irreducible
polynomial representations and the matrix coordinate ring of the standard
quantum group, as constructed by Kashiwara and Lusztig, and the Kazhdan-Lusztig
basis of the Hecke algebra. A positive ($#P$-) formula for the well-known
plethysm constants follows from their conjectural properties and the duality
and reciprocity conjectures in \cite{GCT7}.
