S N orbifolds and string interactions

We study interacting features of S _N orbifold CFTs. Concentrating on characters (associated with S _N Orbifold primaries) we first formulate a novel procedure for evaluating them through {GL}{(∞ )}₊ tracing. The result is a polynomial formula which we show gives results equivalent to those found by Bantay. From this we deduce a hierarchy of commuting Hamiltonians featuring locality in the induced space, and nonlinear string-type interactions.