Associative algebras of Z-graded vertex operator superalgebras and their applications

Let V be a Z-graded vertex operator superalgebra and G a finite automorphism group of V of order T. For g E G and n E T Z+, a series of associative algebras Ag,n(V ) are constructed 1 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 E 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 E G, every irreducible g-twisted V-module is a completely reducible VG-module. & COPY; 2023 Elsevier Inc. All rights reserved.