The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra widehat{mathfrak{sl}₂}

We introduce and study the so-called serpentine representations of the infinite symmetric group $\sinf$, which turn out to be closely related to the basic representation of the affine Lie algebra $\widehat{\mathfrak{sl}_2}$ 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 $\widehat\sl$ and a Schur--Weyl representation of the infinite symmetric group" (arXiv:1403.1558)