Cohomology of the toric arrangement associated with $A_n$

Abstract

We compute the total cohomology of the complement of the toric arrangement associated to the root system $A_n$ as a representation of the corresponding Weyl group via fixed point theory of a "twisted" action of the group. We also provide several proofs of an explicit formula for the Poincar\'e polynomial of the complement of the toric arrangement associated with $A_n$.