A and B irreducible representations?
The traditional labelling of irreducible representations is the following:


A, when rotation around the principal axis is symmetrical
B, when rotation around the principal axis is asymmetrical


You can see, for example, that $C_n$ groups of even order have both A and B representations, while those of odd order cannot feature B representations.

As others have commented, there are additional rules… E for doubly degenerate representations, T for triply degenerate, u and g for parity under inversion (odd and even, respectively), greek capital letters Σ, Π, Δ for infinite groups (C∞v and D∞h).

Finally, if there are several irreducible representations that are not distinguished under those conventions, they are numbered.