  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.
