Launois, Stephane (2007) Combinatorics of Hprimes in quantum matrices. Journal of Algebra, 309 (1). pp. 139167. ISSN 00218693. (doi:https://doi.org/10.1016/j.jalgebra.2006.10.023) (Full text available)
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Official URL http://dx.doi.org/10.1016/j.jalgebra.2006.10.023 
Abstract
For q epsilon C transcendental over Q, we give an algorithmic construction of an orderisomorphism between the set of Hprimes of Oq (Mn (C)) and the subposet S of the (reverse) Bruhat order of the symmetric group S2n 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 Hprimes. More precisely, we establish the following result. Imagine that there is a barrier between positions n and it + 1. Then a 2npermuation sigma epsilon S corresponds to a rank t Hinvariant prime ideal Of Oq (Mn (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 orderisomorphism was conjectured by Goodearl and Lenagan.
Item Type:  Article 

Uncontrolled keywords:  quantum matrices; quantum minors; prime ideals; Bruhat order 
Subjects:  Q Science > QA Mathematics (inc Computing science) 
Divisions:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics 
Depositing User:  Stephane Launois 
Date Deposited:  03 Jun 2008 14:20 UTC 
Last Modified:  28 May 2014 10:56 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/3153 (The current URI for this page, for reference purposes) 
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