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

Abstract

We extend the Dong-Mason theorem on the irreducibility of modules for orbifold vertex algebras from [C. Dong, G. Mason, Duke Math. J. 86 (1997)] 305-321] for 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 $W,W\circ g,\dots ,W\circ g^{p-1}$ 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 $\mathfrak{L}$ such that $W,W\circ g,\dots ,W\circ g^{p-1}$ are Whittaker modules having different Whittaker functions. We present certain applications in the cases of the Heisenberg and Weyl vertex operator algebras.

arXiv comment18 pages, a few changes, new result on complete reducibility added

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• Vertex Algebras and Algebraic Curves
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Cited by in corpus (3)

• On fusion rules and intertwining operators for the Weyl vertex algebra
• The Heisenberg-Virasoro Lie conformal superalgebra
• Simple restricted modules for Neveu-Schwarz algebra