Discrete Series Characters as Lifts from Twostructure Groups
Author:
Rebecca A. Herb
Journal:
Trans. Amer. Math. Soc. 353 (2001), 25572599
MSC (2000):
Primary 22E30, 22E45
Published electronically:
March 16, 2001
MathSciNet review:
1828461
Fulltext PDF Free Access
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Abstract: Let be a connected reductive Lie group with a relatively compact Cartan subgroup. Then it has relative discrete series representations. The main result of this paper is a formula expressing relative discrete series characters on as ``lifts'' of relative discrete series characters on smaller groups called twostructure groups for . The twostructure groups are connected reductive Lie groups which are locally isomorphic to the direct product of an abelian group and simple groups which are real forms of or . They are not necessarily subgroups of , but they ``share'' the relatively compact Cartan subgroup and certain other Cartan subgroups with . The character identity is similar to formulas coming from endoscopic lifting, but the twostructure groups are not necessarily endoscopic groups, and the characters lifted are not stable. Finally, the formulas are valid for nonlinear as well as linear groups.
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Additional Information
Rebecca A. Herb
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email:
rah@math.umd.edu
DOI:
http://dx.doi.org/10.1090/S0002994701028276
PII:
S 00029947(01)028276
Received by editor(s):
June 1, 1999
Published electronically:
March 16, 2001
Additional Notes:
Supported in part by NSF Grant DMS 9705645
Article copyright:
© Copyright 2001
American Mathematical Society
