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Conservation relations for local theta correspondence


Authors: Binyong Sun and Chen-Bo Zhu
Journal: J. Amer. Math. Soc. 28 (2015), 939-983
MSC (2010): Primary 22E46, 22E50
DOI: https://doi.org/10.1090/S0894-0347-2014-00817-1
Published electronically: July 2, 2014
MathSciNet review: 3369906
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Abstract: We prove Kudla-Rallis conjecture on first occurrences of local theta correspondence, for all irreducible dual pairs of type I and all local fields of characteristic zero.


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Binyong Sun
Affiliation: Hua Loo-Keng Key Laboratory of Mathematics, Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, P.R. China
Email: sun@math.ac.cn

Chen-Bo Zhu
Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076
Email: matzhucb@nus.edu.sg

DOI: https://doi.org/10.1090/S0894-0347-2014-00817-1
Keywords: Local theta correspondence, conservation relation, oscillator representation, degenerate principal series
Received by editor(s): September 26, 2012
Received by editor(s) in revised form: January 28, 2014, and May 29, 2014
Published electronically: July 2, 2014
Dedicated: In memory of Stephen Rallis
Article copyright: © Copyright 2014 American Mathematical Society