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Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

Benjamin Cahen (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let G be a quasi-Hermitian Lie group with Lie algebra 𝔤 and K be a compactly embedded subgroup of G . Let ξ 0 be a regular element of 𝔤 * which is fixed by K . We give an explicit G -equivariant diffeomorphism from a complex domain onto the coadjoint orbit 𝒪 ( ξ 0 ) of ξ 0 . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where 𝒪 ( ξ 0 ) is associated with a unitary irreducible representation of G which is holomorphically...

Howe's correspondence for a generic harmonic analyst

M. McKee, T. Przebinda (2010)

Colloquium Mathematicae

The goal of this article is to explain Howe's correspondence to a reader who is not necessarily an expert on representation theory of real reductive groups, but is familiar with general concepts of harmonic analysis. We recall Howe's construction of the oscillator representation, the notion of a dual pair and a few basic and general facts concerning the correspondence.

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