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

Permutation orbifolds of 𝔰𝔩2 vertex operator algebras

“…We can choose generators of the orbifold such that they are primary vectors for all k. Moreover, for k = 1 2 and k = − 2 3 these primaries can be chosen so that they are also highest weight vectors for sl 2 . Their explicit formulas are given in the appendix.…”

“…Let L = √ 2A 2 be a rescaled sl(3) root lattice of type A 2 and V L its vertex algebra constructed as in [14]. This algebra contains three orthogonal conformal vectors ω 1 , ω 2 and ω 3 of central charge 1 2 , 7 10 and 4 5 and thus the lattice vertex algebra contains the triple product L( 1 2 , 0) ⊗ L( 7 10 , 0) ⊗ L( 4 5 , 0) conformally embedded in it. An explicit decomposition of V L with respect to this vertex subalgebra was obtained by Lam and Yamada ([18]).…”

“…Barron and Vander Werf studied twisted modules of cyclic permutation orbifolds of fermionic vertex superalgebras ( [6]) based on an earlier work for vertex algebras ( [7], see also [8]). Adamović, Lam, Pedić and Yu considered modules for certain cyclic orbifolds beyond the category of ordinary modules by considering Whittaker modules ( [1]).…”

Simple restricted modules for Neveu-Schwarz algebra

“…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.…”

A class of super Heisenberg-Virasoro algebras

“…[2, 6-8, 12, 23, 24]). Moreover, Whittaker modules have been investigated in the framework of vertex operator algebra theory (see [2,3,16,32]). Whittaker modules for H were investigated in [25].…”