Winding-invariant prime ideals in quantum 3×3 matrices

A complete determination of the prime ideals invariant under winding automorphisms in the generic 3×3 quantum matrix algebra 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 .