Combinatoric of H-primes in quantum matrices
| dc.creator | Launois, Stéphane | |
| dc.date | 2005-01-01 | |
| dc.date | 2005-02-11 | |
| dc.date.accessioned | 2026-07-07T05:15:46Z | |
| dc.date.available | 2026-07-07T05:15:46Z | |
| dc.description | Let n be a positive integer greater than or equal to 2, and q a complex number, transcendental over Q. In this paper, we give an algorithmic construction of an ordered bijection between the set of H-primes of n \times n quantum matrices 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 n positions. Further, we describe the permutations that correspond via this bijection to rank t H-primes, that is, to those H-invariant prime ideals which contain all (t+1) \times (t+1) quantum minors but not all t \times t quantum minors. More precisely, we establish the following result. Imagine that there is a barrier between positions n and n+1. Then a 2n-permutation σwhich belongs to the sub-poset S corresponds to a rank t H-invariant prime ideal of the algebra of n \times n quantum matrices if and only if the number of integers that are moved by σfrom the right to the left of this barrier is exactly n-t. The existence of such a bijection (with such properties) was conjectured by Goodearl and Lenagan. | |
| dc.description | 27 pages, minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0501010 | |
| dc.identifier | http://arxiv.org/abs/math/0501010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73744 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W35; 20G42; 06A07 | |
| dc.title | Combinatoric of H-primes in quantum matrices | |
| dc.type | text |