Discrete Series Characters as Lifts from Two-structure Groups
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- by Rebecca A. Herb PDF
- Trans. Amer. Math. Soc. 353 (2001), 2557-2599 Request permission
Abstract:
Let $G$ 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 $G$ as “lifts” of relative discrete series characters on smaller groups called two-structure groups for $G$. The two-structure 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 $SL(2, \mathbf {C})$ or $SO(5, \mathbf {C} )$. They are not necessarily subgroups of $G$, but they “share” the relatively compact Cartan subgroup and certain other Cartan subgroups with $G$. The character identity is similar to formulas coming from endoscopic lifting, but the two-structure groups are not necessarily endoscopic groups, and the characters lifted are not stable. Finally, the formulas are valid for non-linear as well as linear groups.References
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Additional Information
- Rebecca A. Herb
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 84600
- Email: rah@math.umd.edu
- Received by editor(s): June 1, 1999
- Published electronically: March 16, 2001
- Additional Notes: Supported in part by NSF Grant DMS 9705645
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 2557-2599
- MSC (2000): Primary 22E30, 22E45
- DOI: https://doi.org/10.1090/S0002-9947-01-02827-6
- MathSciNet review: 1828461