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 Physics, pp 1–43

https://doi.org/10.1007/s00220-019-03328-4

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 ${V_k(sl(2))}$ .

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