"Are you the mayor?"
Translation:Bent u de burgemeester?
It is when you are talking about a profession as such that you omit the article. But here you are talking not about being a mayor as a profession, but rather you are asking who is the mayor of a specific place.
Notice that it is usually the indefinite article (not the definite) that gets omitted. So, for example, you would not translate the "A" in the following English sentences, but you would translate the THE:
I want to be A scientist when I grow up.
I want to be the mayor of Minneaapolis when I grow up.