Generalizations of Cauchy's determinant and Schur's Pfaffian

Masao Ishikawa; Soichi Okada; Hiroyuki Tagawa; Jiang Zeng

doi:10.1016/j.aam.2005.07.001

Generalizations of Cauchy's determinant and Schur's Pfaffian

Masao Ishikawa, Soichi Okada, Hiroyuki Tagawa, Jiang Zeng

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	251-287
Number of pages	37
Journal	Advances in Applied Mathematics
Volume	36
Issue number	3
DOIs	https://doi.org/10.1016/j.aam.2005.07.001
Publication status	Published - Mar 2006
Externally published	Yes

Keywords

Cauchy's Determinant
Pfaffian
Plücker relations
Schur functions

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2005.07.001

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title = "Generalizations of Cauchy's determinant and Schur's Pfaffian",

abstract = "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.",

keywords = "Cauchy's Determinant, Pfaffian, Pl{\"u}cker relations, Schur functions",

author = "Masao Ishikawa and Soichi Okada and Hiroyuki Tagawa and Jiang Zeng",

year = "2006",

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doi = "10.1016/j.aam.2005.07.001",

language = "English",

volume = "36",

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T1 - Generalizations of Cauchy's determinant and Schur's Pfaffian

AU - Ishikawa, Masao

AU - Okada, Soichi

AU - Tagawa, Hiroyuki

AU - Zeng, Jiang

PY - 2006/3

Y1 - 2006/3

N2 - 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.

AB - 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.

KW - Cauchy's Determinant

KW - Pfaffian

KW - Plücker relations

KW - Schur functions

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U2 - 10.1016/j.aam.2005.07.001

DO - 10.1016/j.aam.2005.07.001

M3 - Article

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SN - 0196-8858

VL - 36

SP - 251

EP - 287

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 3

ER -

Generalizations of Cauchy's determinant and Schur's Pfaffian

Abstract

Keywords

ASJC Scopus subject areas

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