a1 Atlas Information Service Co. Ltd, San Kitahama-biru 3-1-6 Kitahama, Chuo-ku, Osaka-shi, Osaka-fu, Japan 541-0041 (email@example.com)
a2 Department of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan (firstname.lastname@example.org)
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
(Received November 27 2000)