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Joint Meeting of AMS, DMV, and ÖMG
June 16-19, 2005
Johannes Gutenberg University
Mainz, Germany

Organizers
Volker Bach, Mainz; Klaus D. Bierstedt, DMV; Susan Friedlander, Associate Secretary, AMS

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Variations on Cauchy's determinant and Schur's Pfaffian
by
Soichi Okada
Nagoya University

We present several identities of Cauchy-type determinants and Schur-type Pfaffians involving generalized Vandermonde determinants. These identities generalize Cauchy's determinant identity for det ( 1/(xi+yj) )1 £ i, j £ n and Schur's Pfaffian identity for Pf ( (xj - xi)/(xj + xi) )1 £ i, j £ 2n. Also we give an elliptic extension of Schur's Pfaffian identity and a Pfaffian-Hafnian analogue of Borchardt's identity. Finally we discuss several applications of these identities.

Date received: March 25, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caql-59.