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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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The Fourier-Jacobi map and small representations
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by Martin H. Weissman PDF
Represent. Theory 7 (2003), 275-299 Request permission

Abstract:

We study the “Fourier-Jacobi” functor on smooth representations of split, simple, simply-laced $p$-adic groups. This functor has been extensively studied on the symplectic group, where it provides the representation-theoretic analogue of the Fourier-Jacobi expansion of Siegel modular forms. Our applications are different from those studied classically with the symplectic group. In particular, we are able to describe the composition series of certain degenerate principal series. This includes the location of minimal and small (in the sense of the support of the local character expansion) representations as spherical subquotients.
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Additional Information
  • Martin H. Weissman
  • Affiliation: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138
  • Address at time of publication: Department of Mathematics, University of California, Berkeley, 940 Evans Hall, Berkeley, California 94704
  • MR Author ID: 718173
  • Email: martinw@math.harvard.edu
  • Received by editor(s): March 7, 2002
  • Received by editor(s) in revised form: September 2, 2002, October 31, 2002, January 2, 2003, and April 23, 2003
  • Published electronically: July 28, 2003
  • Additional Notes: The author was supported in part by a NSF Graduate Research Fellowship during the preparation of this paper.
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 275-299
  • MSC (2000): Primary 20G05, 22E50; Secondary 22E35, 22E10
  • DOI: https://doi.org/10.1090/S1088-4165-03-00197-3
  • MathSciNet review: 1993361