Bessel functions on quaternionic Siegel domains
This article is part of a series of papers by the author on harmonic analysis on Hermitian symmetric spaces. The space under study here is \(G/K\), where \(G\) is the group \(O_ *(4n + 2)\) and \(K\) is a maximal compact subgroup, a Siegel domain of type II. The author considers the Segal-Shale-Weil (or harmonic) representation of \(G\) on a Schrödinger- Fock space (an \(L^ 2\) space of holomorphic functions). Making use of operator-valued Bessel and gamma functions, he obtains the main result of the paper: the Segal-Shale-Weil representation decomposes into a direct sum of irreducible components unitarily equivalent (by means of a Laplace transform) to holomorphic discrete series representations of \(G\).
holomorphic discrete series representations
scientific article; zbMATH DE number 599747