Combinatorics of H-primes in quantum matrices

For q epsilon C transcendental over Q, we give an algorithmic construction of an order-isomorphism between the set of H-primes of O-q (M-n (C)) and the sub-poset S of the (reverse) Bruhat order of the symmetric group S-2n consisting of those permutations that move any integer by no more than it positions. Further, we describe the permutations that correspond via this bijection to rank t H-primes. More precisely, we establish the following result. Imagine that there is a barrier between positions n and it + 1. Then a 2n-permuation sigma epsilon S corresponds to a rank t H-invariant prime ideal Of O-q (M-n (Q) if and only if the number of integers that are moved by sigma from the right to the left of this barrier is exactly n - t. The existence of such an order-isomorphism was conjectured by Goodearl and Lenagan.