一个将量子子式恒等式推广到多参数情形的简单算法

多参数 Manin 矩阵的量子代数

Quantum algebra of multiparameter Manin matrices

本文利用 R-matrix 方法系统研究多参数 Manin 矩阵的量子代数，导出并证明行列式、积和式的多种经典恒等式及 MacMahon 主方程，并将部分结果推广至多参数 $q$-Yangians。

Sklyanin行列式的次要恒等式

Minor identities for Sklyanin determinants

本文利用R矩阵技术研究正交与辛型量子对称空间的不变理论，建立了量子行列式、Sklyanin行列式与量子Pfaffian的联系，并将多种q-恒等式推广至Sklyanin子式，同时给出其准行列式表达。

量子子式的包含行交换原理

Included-row exchange principle for quantum minors

本文的主要定理允许将量子线性群的量子子式之间的一类恒等式推广到类似的恒等式，但所涉及的量子子式的行标号被置换。

Basic quadratic identities on quantum minors

This paper continues an earlier research of the authors on universal quadratic identities (QIs) on minors of quantum matrices. We demonstrate situations when the universal QIs are provided, in a sense, by the ones of four special types (Plucker, co-Plucker, Dodgson identities and quasi-commutation relations on flag and co-flag interval minors).

拟行列式与量子行列式的次恒等式

Minor Identities for Quasideterminants and Quantum Determinants

我们提出了几个涉及非交换一般矩阵的拟子式的恒等式。这些恒等式专门用于量子矩阵，产生各种经典行列式公式的q-类似物。

On universal quadratic identities for minors of quantum matrices

We give a complete combinatorial characterization of homogeneous quadratic relations of "universal character" valid for minors of quantum matrices (more precisely, for minors in the quantized coordinate ring $O_q(M_{m,n}(K))$ of $m\times n$ matrices over a field $K$, where $q\in K^\ast$). This is obtained as a consequence of a study of quantized minors of matrices generated by paths in certain planar graphs, called SE-graphs, generalizing the ones associated with Cauchon diagrams. Our efficient method of verifying universal quadratic identities for minors of quantum matrices is illustrated wit…