The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra $\widehat{{\mathfrak{s}\mathfrak{l}}_2}$

We introduce and study the so-called serpentine representations of the infinite symmetric group $\text{sinf}$, which turn out to be closely related to the basic representation of the affine Lie algebra $\widehat{{\mathfrak{s}\mathfrak{l}}_2}$ and representations of the Virasoro algebra. This is a new version of the manuscript of the same authors “On a relation between the basic representation of the affine Lie algebra $\widehat{\text{sl}}$ and a Schur–Weyl representation of the infinite symmetric group” (arXiv:1403.1558)