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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Dualities for root systems with automorphisms and applications to non-split groups
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by Thomas J. Haines PDF
Represent. Theory 22 (2018), 1-26 Request permission


This article establishes some elementary dualities for root systems with automorphisms. We give several applications to reductive groups over non-archimedean local fields: (1) the proof of a conjecture of Pappas-Rapoport-Smithling characterizing the extremal elements of the $\{ \mu \}$-admissible sets attached to general non-split groups; (2) for quasi-split groups, a simple uniform description of the Bruhat-Tits échelonnage root system $\Sigma _0$, the Knop root system $\widetilde {\Sigma }_0$ and the Macdonald root system $\Sigma _1$, in terms of Galois actions on the absolute roots $\Phi$; and (3) for quasi-split groups, the construction of the geometric basis of the center of a parahoric Hecke algebra, and the expression of certain important elements of the stable Bernstein center in terms of this basis. The latter gives an explicit form of the test function conjecture for general Shimura varieties with parahoric level structure.
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Additional Information
  • Thomas J. Haines
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
  • MR Author ID: 659516
  • Email:
  • Received by editor(s): June 29, 2016
  • Received by editor(s) in revised form: January 23, 2018
  • Published electronically: March 9, 2018
  • Additional Notes: The author’s research was partially supported by NSF DMS-1406787
  • © Copyright 2018 American Mathematical Society
  • Journal: Represent. Theory 22 (2018), 1-26
  • MSC (2010): Primary 20C08, 20G25, 22E50, 17B20; Secondary 11F70, 11G18
  • DOI:
  • MathSciNet review: 3772644