Realizations of Simple Affine Vertex Algebras and Their Modules: The Cases \widehat{sl(2)} and \widehat{osp(1,2)}

Author: Dražen Adamović

Communications in Mathematical Physicspp 1–43

Abstract: We study the embeddings of the simple admissible affine vertex algebras {V_k(sl(2))} and {V_k({osp}(1,2))}, {k \notin {\mathbb Z}_{\ge 0}}, into the tensor product of rational Virasoro and N = 1 Neveu–Schwarz vertex algebra with lattice vertex algebras. By using these realizations we construct a family of weight, logarithmic, and Whittaker {\widehat{sl(2)}} and {\widehat{osp(1,2)}}-modules. As an application, we construct all irreducible degenerate Whittaker modules for {V_k(sl(2))}.