2021/12/16 by Dražen Adamović, Adamovic, Drazen, Veronika Pedić Tomić +1
Mathematics · #17B69 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2112.08725
openalex publication_date 2021/12/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/01
We consider the Whittaker modules M1(λ,μ) for the Weyl vertex algebra M, constructed in arXiv:1811.04649, where it was proved that these modules are irreducible for each finite cyclic orbifold M\Bbb Zn. In this paper, we consider the modules M1(λ,μ) as modules for the \Bbb Z-orbifold of M, denoted by M0. M0 is isomorphic to the vertex algebra \mathcal W1+∞, c=-1 = \mathcal M(2) ⊗ M1(1) which is the tensor product of the Heisenberg vertex algebra M1(1) and the singlet algebra \mathcal M(2). Furthermore, these modules are also modules of the Lie algebra \widehat\mathfrak gl with central charge c=-1. We prove they are reducible as \widehat\mathfrak gl-modules (and therefore also as M0-modules), and we completely describe their irreducible quotients L(d,λ,μ). We show that L(d,λ,μ) in most cases are not tensor product modules for the vertex algebra \mathcal M(2) ⊗ M1(1). Moreover, we show that all constructed modules are typical in the sense that they are irreducible for the Heisenberg-Virasoro vertex subalgebra of \mathcal W1+∞, c=-1.