Generalizations of Cauchy’s Determinant and Schur’s Pfaffian
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چکیده
We present several generalizations of Cauchy’s determinant det (1/(xi + yj)) and Schur’s Pfaffian Pf ((xj − xi)/(xj + xi)) by considering matrices whose entries involve some generalized Vandermonde determinants. Special cases of our formulae include previous formulae due to S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood– Richardson coefficients involving a rectangular partition.
منابع مشابه
ELLIPTIC INTEGRABLE SYSTEMS Generalizations of Cauchy’s Determinant Identity and Schur’s Pfaffian Identity
Abstract We review several determinant and Pfaffian identities, which generalize the evaluation formulae of Cauchy’s determinant det (1/(xi + yj)) and Schur’s Pfaffian Pf ((xj − xi)/(xj + xi)). As a multi-variable generalization, we consider Cauchytype determinants and Schur-type Pfaffians of matrices with entries involving some generalized Vandermonde determinants. Also we give an elliptic gen...
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تاریخ انتشار 2004