Earlier quoted context omitted.
That is just exponentiation, eg squaring. They’re just putting symbols instead of numbers there.
But then they say A + A <= A^2, wouldn’t that be false for a = 1?
In this context, A is a set, and A + A represents the set of all sums of pairs of elements drawn from A.
The paper doesn't use A^2, but rather |A|^2, which is ordinary squaring of an integer. It does use AA, which is the set of products of pairs of elements drawn from A.