量子矩阵中H-素数的组合
Combinatoric of H-primes in quantum matrices
摘要：
设n为大于等于2的正整数，q为复数，是Q上的超越数.本文给出了n个\times n量子矩阵的H-素数集与对称群S_{2n}的（逆）Bruhat序的子偏序集S之间的有序双射的算法构造。进一步，我们描述了通过这个双射对应于秩t H-素数的置换，也就是说，对应于那些包含所有（t+1）\times（t+1）量子子式但不是所有t \times t量子子式的H-不变素理想。更准确地说，我们得出了以下结果。假设在位置n和n+1之间有一个障碍。则属于子偏序集S的一个2n-置换σ对应于n个\times n量子矩阵代数的一个秩t H-不变素理想当且仅当由σ从这个障碍的右边移动到左边的整数的个数正好是n-t。古迪尔和勒纳根证明了这样一个双射的存在（具有这样的性质）。
英文摘要：
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.
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