An elliptic generalization of Schur's Pfaffian identity

被引：10

作者：

Okada, Soichi ^{[1
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

来源：

ADVANCES IN MATHEMATICS | 2006年 / 204卷 / 02期

关键词：

elliptic function; pfaffian; schur function; determinant;

D O I：

10.1016/j.aim.2005.05.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a Pfaffian identity involving elliptic functions, whose rational limit gives a generalization of Schur's Pfaffian identity for Pf ((x(j) - x(i))/(x(j) + x(i))). This identity can be regarded as the Pfaffian counterpart of Frobenius' generalization of Cauchy's determinant identity for det (1 / (x(i) + x(j))). (C) 2005 Elsevier Inc. All rights reserved.

引用

页码：530 / 538

页数：9

共 12 条

[1] [Anonymous], 1990, COURSE MORDERN ANAL
[2] Cauchy A.L., 1841, EXERCISES ANAL PHYS, P151
[3] FROBENIUS G, 1882, J REINE ANGEW MATH, V93, P53
[4] Pfaffian identities: A combinatorial approach
Hamel, AM
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2001, 94 (02) : 205 - 217
[5] ISHIKAWA M, ARXIVMATHCO0312358
[6] ISHIKAWA M, ARXIVMATHCO0411280
[7] Multiple elliptic hypergeometric series. An approach from the Cauchy determinant
Kajihara, Y
Noumi, M
[J]. INDAGATIONES MATHEMATICAE-NEW SERIES, 2003, 14 (3-4): : 395 - 421
[8] KNUTH D, 1996, ELECTRON J COMB, V3, P151
[9] MACDONALD IG, 1995, SYMMETRIC FUNCTIONS
[10] Applications of minor summation formulas to rectangular-shaped representations of classical groups
Okada, S
[J]. JOURNAL OF ALGEBRA, 1998, 205 (02) : 337 - 367

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