Advanced Studies in Pure Mathematics

Minor Summation Formulas of Pfaffians, Survey and A New Identity

Masao Ishikawa and Masato Wakayama

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Abstract

In this paper we treat the minor summation formulas of pfaffians presented in [IW1] and derive several basic formulas concerning pfaffians from it. We also present a pfaffian version of the Plücker relation and give a new pfaffian identity as its application.

Article information

Source
Combinatorial Methods in Representation Theory, K. Koike, M. Kashiwara, S. Okada, I. Terada and H.-F. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2000), 133-142

Dates
Received: 1 March 1999
First available in Project Euclid: 20 August 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1534789258

Digital Object Identifier
doi:10.2969/aspm/02810133

Mathematical Reviews number (MathSciNet)
MR1864479

Zentralblatt MATH identifier
0980.15006

Subjects
Primary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14]
Secondary: 22E46: Semisimple Lie groups and their representations 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

Keywords
Pfaffian generating function Schur’s polynomial partition Plücker’s relation Lewis–Carroll’s formula Frobenius notation

Citation

Ishikawa, Masao; Wakayama, Masato. Minor Summation Formulas of Pfaffians, Survey and A New Identity. Combinatorial Methods in Representation Theory, 133--142, Mathematical Society of Japan, Tokyo, Japan, 2000. doi:10.2969/aspm/02810133. https://projecteuclid.org/euclid.aspm/1534789258


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