EXPLICIT CAPELLI IDENTITIES FOR SKEW SYMMETRIC MATRICES

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