m at h . Q A ] 1 4 Fe b 20 02 Uniform product of A g , n ( V ) for an orbifold model V and G - twisted Zhu algebra Masahiko Miyamoto ∗ and Kenichiro Tanabe

Let V be a vertex operator algebra and G a finite automorphism group of V . For each g ∈ G and nonnegative rational number n ∈ Z/|g|, a g-twisted Zhu algebra Ag,n(V ) plays an important role in the theory of vertex operator algebras, but the given product in Ag,n(V ) depends on the eigenspaces of g. We show that there is a uniform definition of products on V and we introduce a G-twisted Zhu algebra AG,n(V ) which covers all g-twisted Zhu algebras. Let V be simple and let S be a finite set of inequivalent irreducible twisted V -modules which is closed under the action of G. There is a finite dimensional semisimple associative algebra Aα(G,S) for a suitable 2-cocycle naturally determined by the G-action on S. We show that a duality theorem of Schur-Weyl type holds for the actions of Aα(G,S) and V G on the direct sum of twisted V -modules in S as an application of the theory of AG,n(V ). It follows as a natural consequence of the result that for any g ∈ G every irreducible g-twisted V -module is a completely reducible V G-module.