Winding-invariant prime ideals in quantum 3× 3 matrices

A complete determination of the prime ideals invariant under winding auto-morphisms in the generic 3 3 quantum matrix algebra Oq(M3(k)) is obtained. Explicit generating sets consisting of quantum minors are given for all of these primes, thus verifying a general conjecture in the 3 3 case. The result relies heavily on certain tensor product decompositions for winding-invariant prime ideals, developed in an accompanying paper. In addition, new methods are developed here, which show that certain sets of quantum minors, not previously manageable, generate prime ideals in Oq(Mn(k))