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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) (KAR id:7410)


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
DOI/Identification number: 10.1081/AGB-200051150
Uncontrolled keywords: Poly-Bernoulli numbers; Prime ideals; Quantum matrices; Quantum minors; Stirling numbers
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Stephane Launois
Date Deposited: 09 Sep 2008 20:45 UTC
Last Modified: 16 Nov 2021 09:45 UTC
Resource URI: (The current URI for this page, for reference purposes)

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