Rank t H-primes in quantum matrices

Let K be a (commutative) field and consider a nonzero element q in K that is not a root of unity. Goodearl and Lenagan (2002) have shown that the number of H-primes in R = O-q (M-n (K)) that contain all (t + 1) x (t + 1) quantum minors but not all t x t quantum minors is a perfect square. The aim of this paper is to make precise their result. we prove that this number is equal to (t!)S-2(n + 1, t + 1)(2), where S(n + 1, t + 1) denotes the Stirling number of the second kind associated to n + 1 and t + 1. This result was conjectured by Goodearl, Lenagan, and McCammond. The proof involves some closed formulas for the poly-Bernoulli numbers that were established by Kaneko (1997) and Arakawa and Kaneko (1999).