Launois, Stephane (2005) Rank t Hprimes in quantum matrices. Communications in Algebra, 33 (3). pp. 837854. ISSN 00927872. (doi:10.1081/AGB200051150) (KAR id:7410)
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Official URL: http://dx.doi.org/10.1081/AGB200051150 
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 Hprimes in R = Oq (Mn (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!)S2(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 polyBernoulli numbers that were established by Kaneko (1997) and Arakawa and Kaneko (1999).
Item Type:  Article 

DOI/Identification number:  10.1081/AGB200051150 
Uncontrolled keywords:  PolyBernoulli 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:  https://kar.kent.ac.uk/id/eprint/7410 (The current URI for this page, for reference purposes) 
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