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.

中文翻译：

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有限一般线性群表示的 Epsilon 因子

我们使用 Macdonald 对应为有限一般线性群的不可约表示定义 epsilon 因子。这些 epsilon 因子满足乘法性，并且可以表示为高斯和的乘积。张量积 epsilon 因子与 Rankin-Selberg gamma 因子相关，由此我们证明 Rankin-Selberg gamma 因子可以写成高斯和的乘积。外部平方 epsilon 因子与 Jacquet-Shalika 外部平方伽马因子和 Langlands-Shahidi 外部平方伽马因子相关，用于零级超尖点表示。我们证明这些外部平方因子在特殊情况下是一致的。