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invariant differential operator

Proceedings of the Edinburgh Mathematical Society (1)

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EXPLICIT CAPELLI IDENTITIES FOR SKEW SYMMETRIC MATRICES
Kenji Kinoshita, Masato Wakayama
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 2 / June 2002

Published online by Cambridge University Press:

17 June 2002, pp. 449-465
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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