Instantons moduli spaces and W-algebras

Consider the equivariant intersection cohomology group of the Uhlenbeck space with the structure group $G$ (partial compactification of the $G$-instanton moduli spaces over $\mathbf R^4$ with framing). We endow it with a structure of an integral form of the $W$-algebra, at least when $G$ is of type ADE. We have the infinite dimensional $R$-matrix and the Yang–Baxter equation quite naturally, which give us a new view point to the $W$-algebra.