New duality Transformations in Orbifold Theory

We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold $A(H)/H$, where $A(H)$ is the set of all current-algebraic conformal field theories with a finite symmetry group $H \subset Aut(g)$. The permutation orbifolds with $H = Z_\lambda$ and $H = S_3$ are worked out in full as illustrations but the general formalism includes both simple and semisimple $g$. The motivation for this development is the recently-discovered orbifold Virasoro master equation, whose solutions are identified by the duality transformations as sectors of the permutation orbifolds $A(D_\lambda)/Z_\lambda$.