TY - JOUR

T1 - A compound determinant identity for rectangular matrices and determinants of Schur functions

AU - Ishikawa, Masao

AU - Ito, Masahiko

AU - Okada, Soichi

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/10

Y1 - 2013/10

N2 - 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.

AB - 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.

KW - Classical group character

KW - Compound determinant

KW - Minor

KW - Schur function

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U2 - 10.1016/j.aam.2013.08.001

DO - 10.1016/j.aam.2013.08.001

M3 - Article

AN - SCOPUS:84886718637

VL - 51

SP - 635

EP - 654

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

IS - 5

ER -