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

Masao Ishikawa, Masahiko Ito, Soichi Okada

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

A compound determinant identity for minors of rectangular matrices is established. Given an (s+n-1)×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×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.

Original languageEnglish
Pages (from-to)635-654
Number of pages20
JournalAdvances in Applied Mathematics
Volume51
Issue number5
DOIs
Publication statusPublished - Oct 1 2013
Externally publishedYes

Keywords

  • Classical group character
  • Compound determinant
  • Minor
  • Schur function

ASJC Scopus subject areas

  • Applied Mathematics

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