Extended conformal symmetry and recursion formulae for Nekrasov partition function

We derive an infinite set of recursion formulae for Nekrasov instanton partition function for linear quiver U(N) supersymmetric gauge theories in 4D. They have the structure of a deformed version of W1+infinity algebra which is called SHc algebra (or degenerate double affine Hecke algebra) in the literature. The algebra contains W-N algebra with general central charge defined by a parameter beta, which gives the Omega background in Nekrasov's analysis. Some parts of the formulae are identified with the conformal Ward identity for the conformal block function of Toda field theory.