So Mauricio asks, what is the 'A-side' window? I thought I know the answer, a cheap one, not in the form of a generator, but just in terms of a subcategory generated by certain classes of objects. And I am not sure if it is right.

What is the idea? Suppose we know the mirror for $\C^N$, and suppose we know how to take mirror of the B-side CY stacky quotient $[\C^N / G]$.