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On the automorphic theta representation for simply laced groups

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Abstract

We construct an automorphic realization of the minimal representation of a split, simply laced groupG, over a number field. The realization is by a residue, at a certain point, of an Eisenstein series, induced from the Borel subgroup. This residue representation is square integrable and defines the automorphic theta representation. It has “very few” Fourier coefficients, which turn out to have some extra invariance properties.

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Authors and Affiliations

  1. School of Mathematical Sciences The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    David Ginzburg

  2. Department of Mathematics, The Ohio State University, 43210, Columbus, OH, USA

    Stephen Rallis

  3. School of Mathematical Sciences The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    David Soudry

Authors
  1. David Ginzburg
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  2. Stephen Rallis
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  3. David Soudry
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Correspondence to David Ginzburg.

Additional information

This research was supported by the Basic Research Foundation administered by the Israel Academy of Sciences and Humanities.

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Ginzburg, D., Rallis, S. & Soudry, D. On the automorphic theta representation for simply laced groups. Isr. J. Math. 100, 61–116 (1997). https://doi.org/10.1007/BF02773635

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  • DOI: https://doi.org/10.1007/BF02773635

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