The Fourier-Jacobi map and small representations

Author:
Martin H. Weissman

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

Published electronically:
July 28, 2003

MathSciNet review:
1993361

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the ``Fourier-Jacobi'' functor on smooth representations of split, simple, simply-laced -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:
https://doi.org/10.1090/S1088-4165-03-00197-3

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

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.

Article copyright:
© Copyright 2003
American Mathematical Society