Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatoric of H-primes in quantum matrices   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 \sigma which 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 \sigma from 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.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an