Abstract
Let V be a Z-graded vertex operator superalgebra and G a finite automorphism group of V of order T. For g∈G and n∈1TZ+, a series of associative algebras Ag,n(V) are constructed to study the twisted representations of V. In addition, we introduce a G-twisted associative algebra AG,n(V) such that Ag,n(V) is a quotient algebra of AG,n(V) for any g∈G. As an application of the theory of AG,n(V), we obtain a duality theorem of Schur-Weyl type. In particular, for any g∈G, every irreducible g-twisted V-module is a completely reducible VG-module.
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