G-twisted associative algebras of vertex operator superalgebras

Abstract

Let V be a vertex operator superalgebra and G a finite automorphism group of V. Let σ be the order 2 automorphism of V associated with the superstructure of V. A sequence of associative algebras AG,n(V) are constructed to study the twisted representations of V for nonnegative n∈1T′Z where T′ is the order of group generated by G and σ. This result which generalizes many previous results on Zhu's algebras is then used to investigate the super orbifold theory. If V is a simple vertex operator superalgebra and S is a finite set of inequivalent irreducible twisted V-modules which is closed under the action of G, a duality theorem of Schur-Weyl type is obtained for the actions of certain finite dimensional semisimple associated algebra Aα(G,S) and VG on the direct sum of twisted V-modules in S. In particular, for any g∈G every irreducible g-twisted V-module is completely reducible VG-module.