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Realizations of Simple Affine Vertex Algebras and Their Modules: The Cases {;;;widehat{;;;sl(2)};;;};;; s l ( 2 ) ^ and {;;;widehat{;;;osp(1, 2)};;;};;; o s p ( 1 , 2 ) ^

We study the embeddings of the simple admissible affine vertex algebras 𝑉_𝑘(𝑠𝑙(2))$ and 𝑉𝑘(𝑜𝑠𝑝(1, 2)) , 𝑘∉ℤ≥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 𝑠𝑙(2)ˆ and 𝑜𝑠𝑝(1, 2)ˆ -modules. As an application, we construct all irreducible degenerate Whittaker modules for 𝑉𝑘(𝑠𝑙(2)) .

Affine vertex algebras ; realizations ; relaxed modules ; Whittaker modules

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