  A string basis is constructed for each subalgebra of invariants of the
function algebra on the quantum special linear group. By analyzing the string
basis for a particular subalgebra of invariants, we obtain a ``canonical
basis'' for every finite dimensional irreducible
$U_q({\mathfrak{sl}}(n))$-module. It is also shown that the algebra of
functions on any quantum homogeneous space is generated by quantum minors.
