Pfaffians and Representations of the Symmetric Group

Alain Lascoux

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arXiv · math/0610510

Pfaffians and Representations of the Symmetric Group

Alain Lascoux

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Abstract

Pfaffians of matrices with entries z[i,j]/(x\_i+x\_j), or determinants of matrices with entries z[i,j]/(x\_i-x\_j), where the antisymmetrical indeterminates z[i,j] satisfy the Plücker 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.

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BibTeX RIS

Alain Lascoux. 2006-10-17. Pfaffians and Representations of the Symmetric Group. https://arxiv.org/abs/math/0610510

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