The zeta function of Riemann satisfies a well-known functional equation. This functional equation admits a vast generalisation involving the Artin $L$-functions. The epsilon factors for $GL_n$ emerge when this version of the functional equation is formulated. We study the symmetry of these epsilon factors (with respect to symmetric groups) and show that the epsilon factors have just the right amount of symmetry for them to factor through the corresponding extended quotients. The extended quotients play a crucial role in the representation theory of $GL_n$. An example of such an extended quotient is $T / \! / W$ where $T$ is a maximal torus in the Langlands dual group $GL_n(\mathbb{C})$ and $W$ is the Weyl group. I will illustrate this talk with some simple examples.