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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The value of the global intertwining operators on spherical vectors
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by Volker Heiermann
Proc. Amer. Math. Soc. 147 (2019), 115-124
DOI: https://doi.org/10.1090/proc/14208
Published electronically: September 17, 2018
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Abstract:

Let $F$ be a global field, let $G$ be an unramified quasi-split reductive group over $F$, and let $\chi$ be an everywhere unramified automorphic character of a maximal maximally split torus of $G$. Using Langlands-Shahidi theory, we compute the meromorphic function defined by the action of a global standard intertwining operator associated to $\chi$ on a spherical vector and show that the ratio of its poles in the positive Weyl chamber is well behaved.
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Bibliographic Information
  • Volker Heiermann
  • Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
  • MR Author ID: 351327
  • Email: volker.heiermann@univ-amu.fr
  • Received by editor(s): October 4, 2017
  • Received by editor(s) in revised form: May 1, 2018
  • Published electronically: September 17, 2018
  • Additional Notes: The author benefitted from a grant of Agence Nationale de la Recherche with reference ANR-13-BS01-0012 FERPLAY
  • Communicated by: Ken Ono
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 115-124
  • MSC (2010): Primary 11F70; Secondary 11F66, 22E55
  • DOI: https://doi.org/10.1090/proc/14208
  • MathSciNet review: 3876735