Skip to Main Content

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.

 

The Langlands dual and unitary dual of quasi-split $PGSO_8^E$
HTML articles powered by AMS MathViewer

by Caihua Luo PDF
Represent. Theory 24 (2020), 292-322 Request permission

Abstract:

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 $PGSO_8^E$.
References
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22E35
  • Retrieve articles in all journals with MSC (2010): 22E35
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: caihua@chalmers.se
  • 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: https://doi.org/10.1090/ert/545
  • MathSciNet review: 4126655