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) 
N.Tsilevich, A.Vershik
math.RT