Abstract. A complete determination of the prime ideals invariant under win*
*ding auto-
morphisms in the generic 3 x 3 quantum matrix algebra Oq(M3(k)) is obtaine*
*d. Explicit
generating sets consisting of quantum minors are given for all of these pr*
*imes, thus verifying
a general conjecture in the 3 x 3 case. The result relies heavily on certa*