Applications of minor-summation formula. II: Pfaffians and Schur polynomials
type: Item
instance of: scholarly article
title: Applications of minor-summation formula. II: Pfaffians and Schur polynomials
zbMATH Open document ID: 0947.15008
author: Masao Ishikawa
author: Masato Wakayama
published in: Journal of Combinatorial Theory. Series A
publication date: 1999-12-20T00:00:00Z
review text: [For part I see the authors and \textit{S. Okada}, J. Algebras 183, No. 1, 193-216 (1996; Zbl 0857.15005).] In the present part II minor-summation formulas of Pfaffians are derived using new generating functions involving Schur polynomials with two parameters, which have a product representation. The prototype of these formulas is the Littlewood formula [cf. \textit{D. E. Littlewood}, Symmetric functions and Hall polynomials, Second edition, Oxford Univ. Press, Oxford (1950)]. Applying the minor-summation formula developed by the authors [Linear Multilinear Algebra 39, No. 3, 285-305 (1995; Zbl 0830.15011)] the Littlewood formulas may be extended in various directions. The formulas are proved algebraically by evaluating certain Pfaffians and by developing some techniques to compute sub-Pfaffians of a given skew-symmetric matrix.
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 58A17
Mathematics Subject Classification ID: 15A90
Mathematics Subject Classification ID: 81R05
zbMATH DE Number: 1356438
zbMATH Keywords: minor-summation formula
zbMATH Keywords: symmetric functions
zbMATH Keywords: Pfaffians
zbMATH Keywords: Schur polynomials
zbMATH Keywords: Littlewood formula
MaRDI profile type: Publication
OpenAlex ID: W2069583649
cites work: Applications of minor-summation formula. I: Littlewood's formulas
cites work: Minor summation formula of pfaffians
cites work: Minor summation formula of pfaffians and Schur function identities
cites work: New Schur function series
cites work: S-function series
cites work: Nonintersecting paths, pfaffians, and plane partitions
cites work: Two variable Pfaffian identities and symmetric functions
cites work: Q4435456
cites work: New S function series and non-compact Lie groups
DOI: 10.1006/JCTA.1999.2988
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description: scientific article; zbMATH DE number 1356438