Epsilon factors of representations of finite general linear groups

JOURNAL OF NUMBER THEORY

卷:221

Article

Ye, Rongqing¹  Zelingher, Elad² 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Yale Univ, Dept Math, New Haven, CT 06510 USA

关键词: Epsilon factors;    Gamma factors;    Gauss sums;    Finite groups of Lie type;   

DOI  :  10.1016/j.jnt.2020.06.007

来源: Elsevier

【 摘 要 】

We define epsilon factors for irreducible representations of finite general linear groups using Macdonald's correspondence. These epsilon factors satisfy multiplicativity, and are expressible as products of Gauss sums. The tensor product epsilon factors are related to the Rankin-Selberg gamma factors, by which we prove that the Rankin-Selberg gamma factors can be written as products of Gauss sums. The exterior square epsilon factors relate the Jacquet-Shalika exterior square gamma factors and the Langlands-Shahidi exterior square gamma factors for level zero supercuspidal representations. We prove that these exterior square factors coincide in a special case. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free