Classification of irreducible modules of certain subalgebras of free boson vertex algebra

Abstract

Let M(1) be the vertex algebra for a single free boson. We classify irreducible modules of certain vertex subalgebras of M(1) generated by two generators. These subalgebras correspond to the W(2, 2p − 1)-algebras with central charge 1 − 6(p − 1) 2

Vertex Algebras W(p)Amand W(p)Dmand Constant Term Identities

“…+ since it is a Z 2 orbifold of the singlet vertex algebra M (1) [1], which is generated by ω and H = Qe −α . We also determined the structure of Zhu's algebra A(M (1) + ).…”

Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications

“…More precisely, we have: In particular, if we take r = s = − 1 c L,I we get that u = e − α+β c L,I is a highest weight vector of highest weight (1,0). Let…”

“…In particular, in the case of the single boson, the W-algebra W(2, 2p − 1) and the Virasoro vertex algebra of central charge of (1, p)-models are realized as kernels of certain screening operators (cf. [1]). …”

“…[13,15]) and they are useful in the representation theory of W-algebras (for one application see [1]). We shall here only recall that for γ ∈ D, δ ∈ D 0 , γ, δ = −n, n ∈ Z >0 we have…”

A construction of admissible A1(1)-modules of level -Adamović1 2005Journal of Pure and Applied AlgebraSelf Cite44070View full textAdd to dashboardCite

“…In particular, the Weyl vertex algebras correspond to the -system. Quite recently, the work [25] presented a very detailed study of the -systems and its relation to the WZW-model su (2) …”