# 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. (doi:10.1016/j.jalgebra.2006.10.023) (KAR id:3153)

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## Abstract

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 10.1016/j.jalgebra.2006.10.023 quantum matrices; quantum minors; prime ideals; Bruhat order Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Stephane Launois 03 Jun 2008 14:20 UTC 06 May 2020 03:00 UTC https://kar.kent.ac.uk/id/eprint/3153 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-7252-8515