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Pfaffians and Representations of the Symmetric Group

Pfaffians and Representations of the Symmetric Group
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摘要 Pfaffians of matrices with entries z[i, j]/（xi ＋ xj）, or determinants of matrices with entries z[i, j]/（xi - xj）, where the antisymmetrical indeterminates z[i, j] satisfy the Pliicker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young＇s orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, and recover in particular the evaluation of Pfaffians which appeared in the recent literature. Pfaffians of matrices with entries z[i, j]/（xi ＋ xj）, or determinants of matrices with entries z[i, j]/（xi - xj）, where the antisymmetrical indeterminates z[i, j] satisfy the Pliicker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young＇s orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, and recover in particular the evaluation of Pfaffians which appeared in the recent literature.
作者 Alain LASCOUX
机构地区 CNRS
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第12期1929-1950,共22页 数学学报（英文版）
基金 Supported by ANR project BLAN06-2_134516
关键词 PFAFFIANS symmetric group REPRESENTATIONS Pfaffians, symmetric group, representations
分类号 O152.1 [理学—基础数学]
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参考文献25

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Acta Mathematica Sinica,English Series
2009年 第12期

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