Abstract
We follow Jacquet-Shalika [7], Matringe [12] and Cogdell-Matringe [3] to define exterior square gamma factors for irreducible cuspidal representations of \({\rm{G}}{{\rm{L}}_n}({\mathbb{F}_q})\). These exterior square gamma factors are expressed in terms of Bessel functions associated to the cuspidal representations. We also relate our exterior square gamma factors over finite fields to those over local fields through level-zero representations.
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Acknowledgments
We thank our advisors for their tremendous support. We appreciate the first author’s advisor, James Cogdell, for his support and his comments on this paper. We are grateful to the second author’s advisor, David Soudry, for suggesting the problem and for many helpful discussions during our work on the even case. We thank Ofir Gorodetsky for useful discussions.
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Ye, R., Zelingher, E. Exterior square gamma factors for cuspidal representations of GLn: finite field analogs and level-zero representations. Isr. J. Math. 240, 889–934 (2020). https://doi.org/10.1007/s11856-020-2084-y
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DOI: https://doi.org/10.1007/s11856-020-2084-y