Generalizations of Cauchy's determinant and Schur's Pfaffian

Masao Ishikawa, Soichi Okada, Hiroyuki Tagawa, Jiang Zeng

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We present several identities of Cauchy-type determinants and Schur-type Pfaffians involving generalized Vandermonde determinants, which generalize Cauchy's determinant det(1/(xi+yj)) and Schur's Pfaffian Pf((xj-xi)/(xj+xi)). Some special cases of these identities are given by S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood-Richardson coefficients involving a rectangular partition.

Original languageEnglish
Pages (from-to)251-287
Number of pages37
JournalAdvances in Applied Mathematics
Issue number3
Publication statusPublished - Mar 2006
Externally publishedYes


  • Cauchy's Determinant
  • Pfaffian
  • Plücker relations
  • Schur functions

ASJC Scopus subject areas

  • Applied Mathematics


Dive into the research topics of 'Generalizations of Cauchy's determinant and Schur's Pfaffian'. Together they form a unique fingerprint.

Cite this