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

Abstract

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 $x\mapsto gx{g}^t$. 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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References in corpus (1)

• On the principal symbols of $K_{\mathbb{C}}$-invariant differential operators on Hermitian symmetric spaces

Cited by in corpus (1)

• On the principal symbols of $K_{\mathbb{C}}$-invariant differential operators on Hermitian symmetric spaces