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On certain multiplicity one theorems

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Abstract

We prove several multiplicity one theorems in this paper. Fork a local field not of characteristic two, andV a symplectic space overk, any irreducible admissible representation of the symplectic similitude group GSp(V) decomposes with multiplicity one when restricted to the symplectic group Sp(V). We prove the analogous result for GO(V) and O(V), whereV is an orthogonal space overk. Whenk is non-archimedean, we prove the uniqueness of Fourier-Jacobi models for representations of GSp(4), and the existence of such models for supercuspidal representations of GSp(4).

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Authors and Affiliations

  1. Department of Mathematics, The University of Akron, 44325-4002, Akron, OH, USA

    Jeffrey D. Adler

  2. School of Mathematics, Tata Institute of Fundamental Research, 400 005, Mumbai, India

    Dipendra Prasad

Authors
  1. Jeffrey D. Adler
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  2. Dipendra Prasad
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Correspondence to Jeffrey D. Adler.

Additional information

The first-named author was partially supported by the National Security Agency (#MDA904-02-1-0020).

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Adler, J.D., Prasad, D. On certain multiplicity one theorems. Isr. J. Math. 153, 221–245 (2006). https://doi.org/10.1007/BF02771784

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  • DOI: https://doi.org/10.1007/BF02771784

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