# Rank t H-primes in quantum matrices

Launois, Stephane (2005) Rank t H-primes in quantum matrices. Communications in Algebra, 33 (3). pp. 837-854. ISSN 0092-7872. (doi:10.1081/AGB-200051150)

PDF (Rank t H-Primes)
 Preview
Official URL
http://dx.doi.org/10.1081/AGB-200051150

## Abstract

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).

Item Type: Article 10.1081/AGB-200051150 Poly-Bernoulli numbers; Prime ideals; Quantum matrices; Quantum minors; Stirling numbers Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Stephane Launois 09 Sep 2008 20:45 UTC 28 May 2019 13:43 UTC https://kar.kent.ac.uk/id/eprint/7410 (The current URI for this page, for reference purposes)