Bosonizations of ${\widehat{\mathfrak{sl}}}_2$ and Integrable Hierarchies

Bojko Bakalov, Daniel Fleisher

We construct embeddings of ${\widehat{\mathfrak{sl}}}_2$ in lattice vertex algebras by composing the Wakimoto realization with the Friedan-Martinec-Shenker bosonization. The Kac-Waki…