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EXPLICIT CAPELLI IDENTITIES FOR SKEW SYMMETRIC MATRICES

Published online by Cambridge University Press:  17 June 2002

Kenji Kinoshita  and
Masato Wakayama
Kenji Kinoshita
Affiliation:
Atlas Information Service Co. Ltd, San Kitahama-biru 3-1-6 Kitahama, Chuo-ku, Osaka-shi, Osaka-fu, Japan 541-0041 (kinosita@atlas-is.co.jp)
Masato Wakayama
Affiliation:
Department of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan (wakayama@math.kyushu-u.ac.jp)
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Abstract

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The main purpose of this paper is to obtain an explicit Capelli identity relating skew-symmetric matrices under the action of the general linear group $GL_N$. In particular, we give an explicit formula for the skew Capelli element in terms of the trace of powers of a matrix defined by the standard infinitesimal generators of $GL_N$.

AMS 2000 Mathematics subject classification: Primary 17B35. Secondary 17B10; 15A15; 20G05

Keywords

Capelli identityskew Capelli elementPfaffianuniversal enveloping algebrainvariant differential operatorYoung diagram
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 2 , June 2002 , pp. 449 - 465
Copyright
Copyright © Edinburgh Mathematical Society 2002