On a relation between the basic representation of the affine Lie algebra $\widehat\sl$ and a Schur--Weyl representation of the infinite symmetric group

Natalia Tsilevich, Anatoly Vershik

We prove that there is a natural grading-preserving isomorphism of $\sl$-modules between the basic module of the affine Lie algebra $\widehat\sl$ (with the homogeneous grading) and…