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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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