An elliptic generalization of Schur's Pfaffian identity

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• 作者：Soichi Okada
• 关键词：Elliptic function ; Pfaffian ; Schur function ; Determinant
• 刊名：Advances in Mathematics
• 出版年：2006
• 期刊代码：62_00018708
• 类别：mt
• 出版时间：20 August 2006
• 卷：204
• 期：2
• 页码：530-538
• 文件大小：136 K

摘要

We present a Pfaffian identity involving elliptic functions, whose rational limit gives a generalization of Schur's Pfaffian identity for decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4GSTS52-3&_mathId=mml1&_user=10&_cdi=6681&_rdoc=9&_handle=V-WA-A-W-AV-MsSAYVW-UUA-U-AAZCBUYZUA-AAZWYYEVUA-VBBYCAEE-AV-U&_acct=C000050221&_version=1&_userid=10&md5=b9be81887b9cdaaf0b1d6cda601067fb" title="Click to view the MathML source">Pf((x_j-x_i)/(x_j+x_i)). This identity can be regarded as the Pfaffian counterpart of Frobenius’ generalization of Cauchy's determinant identity for decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4GSTS52-3&_mathId=mml2&_user=10&_cdi=6681&_rdoc=9&_handle=V-WA-A-W-AV-MsSAYVW-UUA-U-AAZCBUYZUA-AAZWYYEVUA-VBBYCAEE-AV-U&_acct=C000050221&_version=1&_userid=10&md5=e41cc95b1c374daac9fdd7ffad66b937" title="Click to view the MathML source">det(1/(x_i+x_j)).