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On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebras

We extend the Dong-Mason theorem on irreducibility of modules for orbifold vertex algebras (cf. [18]) to the category of weak modules. Let V be a vertex operator algebra, g an automorphism of order p. Let W be an irreducible weak V–module such that W, W∘g, …, W∘gp−1 are inequivalent irreducible modules. We prove that W is an irreducible weak V〈g〉–module. This result can be applied on irreducible modules of certain Lie algebra L such that W, W∘g, …, W∘gp−1 are Whittaker modules having different Whittaker functions. We present certain applications in the cases of the Heisenberg and Weyl vertex operator algebras.

vertex algebra ; Whittaker module, orbifold vertex algebra, Weyl vertex algebra ; Heisenberg vertex algebra

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