Pfaffians and Representations of the Symmetric Group

被引：0

作者：

Alain LASCOUX

机构：

[1] CNRS,IGM,UniversiteParis-Est

来源：

Acta Mathematica Sinica(English Series) | 2009年 / 25卷 / 12期

关键词：

Pfaffians; symmetric group; representations;

D O I：

暂无

中图分类号：

O152.1 [有限群论];

学科分类号：

070104 ;

摘要：

<正> Pfaffians of matrices with entries z[i, j]/（xi + xj）, or determinants of matrices with entriesz[i,j]/（xi-xj）, where the antisymmetrical indeterminates z[i, j] satisfy the Pliicker relations, can beidentified with a trace in an irreducible representation of a product of two symmetric groups. UsingYoung's orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, andrecover in particular the evaluation of Pfaffians which appeared in the recent literature.

引用

页码：1929 / 1950

页数：22

共 10 条

[1]

Minor summation formula and a proof of Stanley’s open problem[J] . Masao Ishikawa.The Ramanujan Journal . 2008 (2)

[2]

Advanced determinant calculus: A complement[J] . C. Krattenthaler.Linear Algebra and Its Applications . 2005

[3]

Enumeration of symmetry classes of alternating sign matrices and characters of classical groups[J] . Soichi Okada.Journal of Algebraic Combinatorics . 2006 (1)

[4] Symmetry classes of alternating-sign matrices under one roof [J].

Kuperberg, G .

ANNALS OF MATHEMATICS, 2002, 156 (03) :835-866

[5]

A new approach to representation theory of symmetric groups[J] . Andrei Okounkov,Anatoly Vershik.Selecta Mathematica . 1996 (4)

[6] Two variable Pfaffian identities and symmetric functions [J].

Sundquist, T .

JOURNAL OF ALGEBRAIC COMBINATORICS, 1996, 5 (02) :135-148

[7]

On Giambelli's theorem on complete correlations[J] . D. Laksov,A. Lascoux,A. Thorup.Acta Mathematica . 1989 (1)

[8]

On certain aggregates of determinant minors .2 Muir,T. Proc.R.Soc.Edinburgh . 1900

[9]

Young,A. The collected papers of Alfred Young . 1977

[10]

Izergin-Korepin determinant reloaded .2 Stroganov,Yu.G. .

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