Explicit Hilbert spaces for certain unipotent representations III

Alexander Dvorsky, Siddhartha Sahi

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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

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Keywords

  • Jordan algebra
  • Spherical vector
  • Unipotent representation

ASJC Scopus subject areas

  • Analysis

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