A compound determinant identity for rectangular matrices and determinants of Schur functions
A compound determinant identity for rectangular matrices and determinants of Schur functions
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矩形矩阵的复合行列式恒等式和 Schur 函数的行列式
DOI：
10.1016/j.aam.2013.08.001
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发表时间：
2013
影响因子：
1.1
通讯作者：
and S. Okada
中科院分区：
文献类型：
--
作者：
M. Ishikawa;M. Ito;and S. Okada
建立了矩形矩阵子式的一个复合行列式恒等式。给定一个（s+ n− 1）× sn矩阵A有s个n列的块，我们考虑A的子式，在每个块中选取最多s个部分的弱合成所指定的第一个连续列，并证明了A的这样的n× n子式的复合行列式等于A的s+ n− 1个部分与s个部分的合成所对应的极大子式的乘积.作为应用，我们得到了经典群特征标的行列式的Vandermonde型乘积估计，包括Schur函数。
A compound determinant identity for minors of rectangular matrices is established. Given an (s+ n− 1)× s n matrix A with s blocks of n columns, we consider minors of A by picking up in each block the first consecutive columns specified by weak compositions at most s parts, and prove that the compound determinant of such n× n minors of A is equal to the product of maximal minors of A corresponding to compositions of s+ n− 1 with s parts. As an application, we obtain Vandermonde type product evaluations of determinants of classical group characters, including Schur functions.