The FourierJacobi map and small representations
Author:
Martin H. Weissman
Journal:
Represent. Theory 7 (2003), 275299
MSC (2000):
Primary 20G05, 22E50; Secondary 22E35, 22E10
Published electronically:
July 28, 2003
MathSciNet review:
1993361
Fulltext PDF Free Access
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Abstract: We study the ``FourierJacobi'' functor on smooth representations of split, simple, simplylaced adic groups. This functor has been extensively studied on the symplectic group, where it provides the representationtheoretic analogue of the FourierJacobi 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:
http://dx.doi.org/10.1090/S1088416503001973
PII:
S 10884165(03)001973
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
