論文

査読有り
2013年10月

A compound determinant identity for rectangular matrices and determinants of Schur functions

ADVANCES IN APPLIED MATHEMATICS
  • Masao Ishikawa
  • ,
  • Masahiko Ito
  • ,
  • Soichi Okada

51
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
DOI
https://doi.org/10.1016/j.aam.2013.08.001
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000327113000007&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.aam.2013.08.001
  • ISSN : 0196-8858
  • eISSN : 1090-2074
  • Web of Science ID : WOS:000327113000007

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