Explicit Hilbert spaces for certain unipotent representations III

Alexander Dvorsky, Siddhartha Sahi

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this paper we construct a family of small unitary representations for real semisimple Lie groups associated with Jordan algebras. These representations are realized on L2-spaces of certain orbits in the Jordan algebra. The representations are spherical and one of our key results is a precise L2-estimate for the Fourier transform of the spherical vector. We also consider the tensor products of these representations and describe their decomposition.

Original languageEnglish (US)
Pages (from-to)430-456
Number of pages27
JournalJournal of Functional Analysis
Volume201
Issue number2
DOIs
StatePublished - Jul 10 2003

Fingerprint

Jordan Algebra
Hilbert space
Semisimple Lie Group
Unitary Representation
Tensor Product
Fourier transform
Orbit
Decompose
Estimate
Family

Keywords

  • Jordan algebra
  • Spherical vector
  • Unipotent representation

ASJC Scopus subject areas

  • Analysis

Cite this

Explicit Hilbert spaces for certain unipotent representations III. / Dvorsky, Alexander; Sahi, Siddhartha.

In: Journal of Functional Analysis, Vol. 201, No. 2, 10.07.2003, p. 430-456.

Research output: Contribution to journalArticle

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