We discuss some aspects of the representation theory of the deformed Virasoro algebra Vir(p,q). In particular, we give a proof of the formula for the Kac determinant and then determine the center of Vir(p,q) for q a primitive N-th root of unity. We derive explicit expressions for the generators of the center in the limit t=q p^{-1}-> infty and elucidate the connection to the Hall-Littlewood symmetric functions. Furthermore, we argue that for q a primitive N-th root of unity the algebra describes `Gentile statistics' of order N-1, i.e., a situation in which at most N-1 particles can occupy the same state.
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