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Topology on the unitary dual of completely solvable Lie groups
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Detlev Poguntke
Published/Copyright:
August 16, 2015
Abstract
It was one of great successes of Kirillov's orbit method to see that the unitary dual of an exponential Lie group is in bijective correspondence with the orbit space associated with the linear dual of the Lie algebra of the group in question. To show that this correspondence is an homeomorphism turned out to be unexpectedly difficult. Only in 1994 H. Leptin and J. Ludwig gave a proof using the notion of variable groups. In this article their proof in the case of completely solvable Lie group is reorganized, some “philosophy” and some new arguments are added. The purpose is to contribute to a better understanding of this proof.
Keywords: Exponential Lie groups; variable groups; irreducible unitary
representations; unitary dual; orbit method; Kirillov conjecture; C*-algebras; positive functionals
Received: 2014-11-10
Revised: 2015-5-11
Accepted: 2015-5-11
Published Online: 2015-8-16
Published in Print: 2015-10-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- Some questions related to the Bergman projection in symmetric domains
- Some uncertainty principles for diamond Lie groups
- Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
- Topology on the unitary dual of completely solvable Lie groups
- Rayleigh theorem, projection of orbital measures and spline functions
Keywords for this article
Exponential Lie groups;
variable groups;
irreducible unitary
representations;
unitary dual;
orbit method;
Kirillov conjecture;
C*-algebras;
positive functionals
Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- Some questions related to the Bergman projection in symmetric domains
- Some uncertainty principles for diamond Lie groups
- Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
- Topology on the unitary dual of completely solvable Lie groups
- Rayleigh theorem, projection of orbital measures and spline functions
