Generating function for GL_n-invariant differential operators in the skew Capelli identity

Details Generating function for GL_n-invariant differential operators in the skew Capelli identity Generating function for GL_n-invariant differential operators in the skew Capelli identity

2008-03-10

arxiv.org/abs/0803.1339v2

Mathematics

Representation Theory

Changed content; 10 pages, no figure

Scientific paper

Let Alt_n be the vector space of all alternating n-by-n complex matrices, on which the complex general linear group GL_n acts by $x \mapsto g x g^t$. The aim of this paper is to show that Pfaffian of a certain matrix whose entries are multiplication operators or derivations acting on polynomials on Alt_n provides a generating function for the GL_n-invariant differential operators that play a role in the skew Capelli identity, with coefficients the Hermite polynomials.

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