Free field realization of the level-2 elliptic algebra $U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )*)$

Abstract

We give a level-2 representation of the elliptic algebra $U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}_2 })$ in terms of one free boson and one free fermion. We show that $U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )$-modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the coset $(\mathfrak{s}\mathfrak{l}_2 )_2 \oplus (\mathfrak{s}\mathfrak{l}_2 )_{r - 4} /(\mathfrak{s}\mathfrak{l}_2 )_{r - 2}$.