Certain hat{sl}_2-modules admit Wakimoto realizations at critical and non-critical levels; simple quotients at critical level match known irreducible Wakimoto modules, and some Wakimoto modules are generalized as Whittaker modules.
Adamovi´ c, Lie superalgebras and irreducibility ofA (1) 1 - modules at the critical level , Communications in Mathematical Physics 270 (2007) 141–161
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Irreducibility of Certain $\widehat{\mathfrak{sl}}_2$-Modules of Wakimoto Type
Certain hat{sl}_2-modules admit Wakimoto realizations at critical and non-critical levels; simple quotients at critical level match known irreducible Wakimoto modules, and some Wakimoto modules are generalized as Whittaker modules.