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The Fourier-Jacobi map and small representations

Author(s): Martin H. Weissman
Journal: Represent. Theory 7 (2003), 275-299.
MSC (2000): Primary 20G05, 22E50; Secondary 22E35, 22E10
Posted: July 28, 2003
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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
Email: martinw@math.harvard.edu

DOI: 10.1090/S1088-4165-03-00197-3
PII: S 1088-4165(03)00197-3
Keywords: Representation theory
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
Posted: July 28, 2003
Additional Notes: The author was supported in part by a NSF Graduate Research Fellowship during the preparation of this paper.
Copyright of article: Copyright 2003, American Mathematical Society

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