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Coadjoint orbits of stepwise square integrable representations


Authors: Ingrid Beltiţă and Daniel Beltiţă
Journal: Proc. Amer. Math. Soc. 144 (2016), 1343-1350
MSC (2010): Primary 22E45; Secondary 47G30, 47B10
DOI: https://doi.org/10.1090/proc/12761
Published electronically: June 30, 2015
MathSciNet review: 3447684
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Abstract: Nilpotent Lie groups with stepwise square integrable representations were recently investigated by J.A. Wolf. We give an alternative approach to these representations by relating them to the stratifications of the duals of nilpotent Lie algebras, thus proving that they correspond to a subset with relative Hausdorff topology, dense interior, and total Plancherel measure in the unitary dual of the Lie group under consideration.


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Additional Information

Ingrid Beltiţă
Affiliation: Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania
Email: Ingrid.Beltita@imar.ro, ingrid.beltita@gmail.com

Daniel Beltiţă
Affiliation: Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania
Email: Daniel.Beltita@imar.ro, beltita@gmail.com

DOI: https://doi.org/10.1090/proc/12761
Keywords: Square integrable representation, semidirect product, nilpotent Lie group
Received by editor(s): November 4, 2014
Received by editor(s) in revised form: February 1, 2015
Published electronically: June 30, 2015
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2015 American Mathematical Society