Double quantization of Seiberg-Witten geometry and W-algebras

We show that the double quantization of Seiberg-Witten spectral curve for $\mathrm{\Gamma }$-quiver gauge theory defines the generating current of W$(\mathrm{\Gamma })$-algebra in the free field realization. We also show that the partition function is given as a correlator of the corresponding W$(\mathrm{\Gamma })$-algebra, which is equivalent to the AGT relation under the gauge/quiver (spectral) duality.