Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups
We propose an approach, via relative trace formulae, toward the global restriction problem involving Bessel or Fourier–Jacobi periods on unitary groups U[subscript n] × U[subscript m], generalizing the work of Jacquet–Rallis for m = n − 1 (which is a Bessel period). In particular, when m = 0, we re...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/104373 https://orcid.org/0000-0002-5871-1409 |
| _version_ | 1826216792745312256 |
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| author | Liu, Yifeng |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Liu, Yifeng |
| author_sort | Liu, Yifeng |
| collection | MIT |
| description | We propose an approach, via relative trace formulae, toward the global restriction problem involving Bessel or Fourier–Jacobi periods on unitary groups U[subscript n] × U[subscript m], generalizing the work of Jacquet–Rallis for m = n − 1 (which is a Bessel period). In particular, when m = 0, we recover a relative trace formula proposed by Flicker concerning Kloosterman/Fourier integrals on quasi-split unitary groups. As evidences for our approach, we prove the vanishing part of the fundamental lemmas in all cases, and the full lemma for U[subscript n] × U[subscript n]. |
| first_indexed | 2024-09-23T16:53:31Z |
| format | Article |
| id | mit-1721.1/104373 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:53:31Z |
| publishDate | 2016 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1043732022-09-29T22:13:19Z Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups Liu, Yifeng Massachusetts Institute of Technology. Department of Mathematics Liu, Yifeng We propose an approach, via relative trace formulae, toward the global restriction problem involving Bessel or Fourier–Jacobi periods on unitary groups U[subscript n] × U[subscript m], generalizing the work of Jacquet–Rallis for m = n − 1 (which is a Bessel period). In particular, when m = 0, we recover a relative trace formula proposed by Flicker concerning Kloosterman/Fourier integrals on quasi-split unitary groups. As evidences for our approach, we prove the vanishing part of the fundamental lemmas in all cases, and the full lemma for U[subscript n] × U[subscript n]. National Science Foundation (U.S.). (grant DMS–1302000) 2016-09-22T20:34:03Z 2016-09-22T20:34:03Z 2014-03 2012-12 2016-08-18T15:24:24Z Article http://purl.org/eprint/type/JournalArticle 0025-2611 1432-1785 http://hdl.handle.net/1721.1/104373 Liu, Yifeng. “Relative Trace Formulae toward Bessel and Fourier–Jacobi Periods on Unitary Groups.” Manuscripta Mathematica 145.1–2 (2014): 1–69. https://orcid.org/0000-0002-5871-1409 en http://dx.doi.org/10.1007/s00229-014-0666-x Manuscripta Mathematica Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Liu, Yifeng Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups |
| title | Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups |
| title_full | Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups |
| title_fullStr | Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups |
| title_full_unstemmed | Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups |
| title_short | Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups |
| title_sort | relative trace formulae toward bessel and fourier jacobi periods on unitary groups |
| url | http://hdl.handle.net/1721.1/104373 https://orcid.org/0000-0002-5871-1409 |
| work_keys_str_mv | AT liuyifeng relativetraceformulaetowardbesselandfourierjacobiperiodsonunitarygroups |