Howe's correspondence for a generic harmonic analyst
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 539-557 MSC: Primary 22E45; Secondary 22E46. DOI: 10.4064/cm118-2-10
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.