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On S-matrix, and fusion rules for irreducible VG-modules

Abstract

Let V be a simple vertex operator algebra, and G a finite automorphism group of V such that VG is regular. The definition of entries in S-matrix on VG is discussed, and then is extended. The set of VG-modules can be considered as a unitary space. In this paper, we obtain some connections between V-modules and VG-modules over that unitary space. As an application, we determine the fusion rules for irreducible VG-modules which occur as submodules of irreducible V-modules by the fusion rules for irreducible V-modules and by the structure of G.

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