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

In this paper, we give a construction of simple modules generalizing both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We establish a 1-1 correspondence between simple restricted Neveu-Schwarz modules and simple modules of a family of finite dimensional solvable Lie superalgebras associated to the Neveu-Schwarz algebra. Moreover, for two of these superalgebras all simple modules are classified.

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“…2 )V = 0. In this case V becomes a simple b (1) -module. The proposition follows from Proposition 5.1.…”

Section: Characterization Of Simple Restricted G-modulesmentioning

confidence: 99%

“…This is part of our motivation for this paper. Whittaker modules have been studied in the framework of vertex operator algebra theory in [1,2,18,35]. Irreducibility of certain weak modules for cyclic orbifold vertex algebras have been established.…”

Section: Introductionmentioning

confidence: 99%

Simple restricted modules for Neveu-Schwarz algebra

2020

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“…[8]) and modules of Whittaker type (cf. [7]). Since W k is an orbifold of the Weyl vertex algebras, Whittaker and weight modules are also W k -modules.…”

Section: 2mentioning

confidence: 99%

Classification of irreducible modules for Bershadsky–Polyakov algebra at certain levels

Adamović

Kontrec

2020

J. Algebra Appl.

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We study the representation theory of the Bershadsky-Polyakov algebra W k = W k (sl 3 , f θ ). In particular, Zhu algebra of W k is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category O for the Bershadsky-Polyakov algebra W k for k = −5/3, −9/4, −1, 0. In the case k = 0 we show that the Zhu algebra A(W k ) has 2-dimensional indecomposable modules.

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