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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.

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Coincidence of algebraic and smooth theta correspondences
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by YiXin Bao and BinYong Sun PDF
Represent. Theory 21 (2017), 458-466 Request permission

Abstract:

An “automatic continuity” question has naturally occurred since Roger Howe established the local theta correspondence over $\mathbb R$: Does the algebraic version of local theta correspondence over $\mathbb R$ agree with the smooth version? We show that the answer is yes, at least when the concerning dual pair has no quaternionic type I irreducible factor.
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Additional Information
  • YiXin Bao
  • Affiliation: School of Sciences, Harbin Institute of Technology, Shenzhen, 518055, China
  • MR Author ID: 947459
  • Email: baoyixin@hit.edu.cn
  • BinYong Sun
  • Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences –and– School of Mathematics, University of Chinese Academy of Sciences, Beijing, 100190, China
  • MR Author ID: 805605
  • Email: sun@math.ac.cn
  • Received by editor(s): January 13, 2017
  • Received by editor(s) in revised form: May 26, 2017, and August 10, 2017
  • Published electronically: November 1, 2017
  • Additional Notes: The second author was supported in part by the National Natural Science Foundation of China (No. 11525105, 11688101, 11621061 and 11531008).
  • © Copyright 2017 American Mathematical Society
  • Journal: Represent. Theory 21 (2017), 458-466
  • MSC (2010): Primary 22E46, 22E50
  • DOI: https://doi.org/10.1090/ert/508
  • MathSciNet review: 3718456