2013年10月
A compound determinant identity for rectangular matrices and determinants of Schur functions
ADVANCES IN APPLIED MATHEMATICS
- ,
- ,
- 巻
- 51
- 号
- 5
- 開始ページ
- 635
- 終了ページ
- 654
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.aam.2013.08.001
- 出版者・発行元
- ACADEMIC PRESS INC ELSEVIER SCIENCE
A compound determinant identity for minors of rectangular matrices is established. Given an (s + n - 1) x sn 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 x 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. (C) 2013 Elsevier Inc. All rights reserved.
- リンク情報
- ID情報
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- DOI : 10.1016/j.aam.2013.08.001
- ISSN : 0196-8858
- eISSN : 1090-2074
- Web of Science ID : WOS:000327113000007