量子矩阵中的环面不变素理想、完全非负胞腔和辛叶
Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves
摘要：
给定大小的量子矩阵的代数通过自同构支持有理环面作用。它遵循工作的Letzter和第一个命名的作者，以了解总理和原始谱这个代数，第一步是要了解的素理想是不变的环面行动。本文证明了量子子式族是属于量子矩阵代数的给定环面不变素理想的所有量子子式的集合当且仅当相应的子式族在适当大小的完全非负实矩阵空间中定义了一个非空的完全非负胞腔.作为推论，在量子化参数$q$超越$\mathbb{Q}$的情况下，我们得到了量子矩阵环面不变素理想的量子子式的显式生成集.
英文摘要：
The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the prime and primitive spectra of this algebra, the first step is to understand the prime ideals that are invariant under the torus action. In this paper, we prove that a family of quantum minors is the set of all quantum minors that belong to a given torus-invariant prime ideal of a quantum matrix algebra if and only if the corresponding family of minors defines a non-empty totally nonnegative cell in the space of totally nonnegative real matrices of the appropriate size. As a corollary, we obtain explicit generating sets of quantum minors for the torus-invariant prime ideals of quantum matrices in the case where the quantisation parameter $q$ is transcendental over $\mathbb{Q}$.
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