Applications of Minor-Summation Formula II. Pfaffians and Schur Polynomials

Masao Ishikawa; Masato Wakayama

doi:10.1006/jcta.1999.2988

Applications of Minor-Summation Formula II. Pfaffians and Schur Polynomials

Masao Ishikawa, Masato Wakayama

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

16 Citations (Scopus)

Abstract

The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.

Original language	English
Pages (from-to)	136-157
Number of pages	22
Journal	Journal of Combinatorial Theory. Series A
Volume	88
Issue number	1
DOIs	https://doi.org/10.1006/jcta.1999.2988
Publication status	Published - Oct 1999
Externally published	Yes

Keywords

Character
Generating function
Partition
Pfaffian
Schur polynomial

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1006/jcta.1999.2988

Cite this

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abstract = "The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.",

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N2 - The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.

AB - The purpose of this paper is, to establish, by extensive use of the minor summation formula of pfaffians exploited in (Ishikawa, Okada, and Wakayama, J. Algebra 183, 193-216) certain new generating functions involving Schur polynomials which have a product representation. This generating function gives an extension of the Littlewood formula. During the course of the proof we develop some techniques for computing sub-Pfaffians of a given skew-symmetric matrix. After the proof we present an open problem which generalizes our formula.

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KW - Generating function

KW - Partition

KW - Pfaffian

KW - Schur polynomial

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Applications of Minor-Summation Formula II. Pfaffians and Schur Polynomials

Abstract

Keywords

ASJC Scopus subject areas

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