Combinatorics of H-primes in quantum matrices

Launois, Stephane (2007) Combinatorics of H-primes in quantum matrices. Journal of Algebra, 309 (1). pp. 139-167. ISSN 0021-8693 . (Full text available)

PDF (Combinatorics of H-primes)
Download (349kB)
Official URL


For q epsilon C transcendental over Q, we give an algorithmic construction of an order-isomorphism between the set of H-primes of O-q (M-n (C)) and the sub-poset S of the (reverse) Bruhat order of the symmetric group S-2n 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 H-primes. More precisely, we establish the following result. Imagine that there is a barrier between positions n and it + 1. Then a 2n-permuation sigma epsilon S corresponds to a rank t H-invariant prime ideal Of O-q (M-n (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 order-isomorphism 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 > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Stephane Launois
Date Deposited: 03 Jun 2008 14:20
Last Modified: 28 May 2014 10:56
Resource URI: (The current URI for this page, for reference purposes)
  • Depositors only (login required):