Coincidence of algebraic and smooth theta correspondences
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- by YiXin Bao and BinYong Sun
- Represent. Theory 21 (2017), 458-466
- DOI: https://doi.org/10.1090/ert/508
- Published electronically: November 1, 2017
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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.References
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Bibliographic 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