On existence of generic cusp forms on semisimple algebraic groups
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- by Allen Moy and Goran Muić PDF
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Abstract:
In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for a general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean group $G_\infty$ is not compact. When $G$ is quasi-split over $k$, we obtain a result on existence of generic cuspidal automorphic representations which generalize results of Vignéras, Henniart, and Shahidi. We also discuss: (i) the existence of cuspidal automorphic forms with non-zero Fourier coefficients for congruence of subgroups of $G_\infty$, and (ii) applications related to the work of Bushnell and Henniart on generalized Whittaker models.References
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Additional Information
- Allen Moy
- Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
- MR Author ID: 127665
- Email: amoy@ust.hk
- Goran Muić
- Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
- Email: gmuic@math.hr
- Received by editor(s): September 17, 2015
- Received by editor(s) in revised form: September 25, 2016
- Published electronically: January 18, 2018
- Additional Notes: The first author acknowledges Hong Kong Research Grants Council grant CERG #603813
The second author acknowledges Croatian Science Foundation grant no. 9364 - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 4731-4757
- MSC (2010): Primary 11E70, 22E50
- DOI: https://doi.org/10.1090/tran/7081
- MathSciNet review: 3812094