Fourier coefficients for theta representations on covers of general linear groups
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Abstract:
We show that the theta representations on certain covers of general linear groups support certain types of unique functionals. The proof involves two types of Fourier coefficients. The first are semi-Whittaker coefficients, which generalize coefficients introduced by Bump and Ginzburg for the double cover. The covers for which these coefficients vanish identically (resp. do not vanish for some choice of data) are determined in full. The second are the Fourier coefficients associated with general unipotent orbits. In particular, we determine the unipotent orbit attached, in the sense of Ginzburg, to the theta representations.References
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Additional Information
- Yuanqing Cai
- Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467-3806
- Address at time of publication: Department of Mathematics, The Weizmann Institute of Science, Rehovot, 7610001, Israel
- Email: yuanqing.cai@weizmann.ac.il
- Received by editor(s): October 26, 2016
- Received by editor(s) in revised form: August 3, 2017, and October 3, 2017
- Published electronically: March 7, 2019
- Additional Notes: This work was supported by the National Science Foundation, grant number 1500977
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 7585-7626
- MSC (2010): Primary 11F70; Secondary 11F30, 11F27
- DOI: https://doi.org/10.1090/tran/7429
- MathSciNet review: 3955529