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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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.


The Langlands dual and unitary dual of quasi-split $PGSO_8^E$
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by Caihua Luo PDF
Represent. Theory 24 (2020), 292-322 Request permission


This paper serves two purposes, by adopting the classical Casselman–Tadi$\acute {c}$’s Jacquet module machine and the profound Langlands–Shahidi theory, we first determine the explicit Langlands classification for quasi-split groups $PGSO^E_8$ which provides a concrete example to guess the internal structures of parabolic inductions. Based on the classification, we further sort out the unitary dual of $PGSO^E_8$ and compute the Aubert duality which could shed light on the final answer of Arthur’s conjecture for $PGSO_8^E$. As an essential input to obtain a complete unitary dual, we also need to determine the local poles of triple product L-functions which is done in the appendix. As a byproduct of the explicit unitary dual, we verified Clozel’s finiteness conjecture of special exponents and Bernstein’s unitarity conjecture concerning AZSS duality for $PGSO_8^E$.
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Additional Information
  • Caihua Luo
  • Affiliation: Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Chalmers Tvärgata 3, SE-412 96 Göteborg, Sweden
  • MR Author ID: 1253923
  • ORCID: 0000-0001-9523-638X
  • Email:
  • Received by editor(s): May 5, 2019
  • Received by editor(s) in revised form: December 25, 2019, and February 21, 2020
  • Published electronically: July 21, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 292-322
  • MSC (2010): Primary 22E35
  • DOI:
  • MathSciNet review: 4126655