The Bessel-Plancherel theorem and applications
Raul Gomez

TL;DR
This paper explores the Bessel-Plancherel theorem for Lie groups of tube type, characterizes Bessel models of induced representations, and applies these results to compute measures and relate them via Howe's dual pairs.
Contribution
It provides a classification of Bessel models, establishes a local multiplicity one theorem, and connects Bessel-Plancherel measures across different groups using Howe's duality.
Findings
Classification of simple Lie groups of tube type.
Characterization of Bessel models for induced representations.
Calculation of Bessel-Plancherel measure for groups of tube type.
Abstract
Let be a simple Lie Group with finite center, and let be a maximal compact subgroup. We say that is a Lie group of tube type if is a hermitian symmetric space of tube type. For such a Lie group , we can find a parabolic subgroup , with given Langlands decomposition, such that is abelian, and admits a generic character with compact stabilizer. We will call any parabolic subgroup satisfying this properties a Siegel parabolic. Let be an admissible, smooth, Fr\'echet representation of a Lie group of tube type , and let be a Siegel parabolic subgroup. If is a generic character of , let be the space of Bessel models of . After describing the classification of all the simple Lie groups of tube type, we will give a…
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Geometry and complex manifolds
