In this paper the authors propose a finite analog of the AGT conjecture. This conjecture implies the existence of certain structures on the equivariant intersection cohomology of the Uhlenbeck partial compactification of the moduli space of framed \(G\)-bundles on \(\mathbb{P}^{2}\). More precisely, it predicts the existence of an action of the corresponding \(W\)-algebra on the above cohomology, satisfying certain properties. They replace the Uhlenbeck space with the space of based quasi-maps from \(\mathbb{P}^{1}\) to any partial flag variety \(G/P\) of \(G\) and conjecture that is equivariant intersection cohomology carries an action of the infinite \(W\)-algebra \(U(\mathfrak{g}, e)\) associated with the principal nilpotent element in the Lie algebra of the Levi subgroup of \(P\). From the physical point of view this conjecture relates a \(4\)-dimensional super-symmetric gauge theory for a gauge group \(G\) with certain \(2\)-dimensional conformal field theory. Initially the authors recall the basic definitions about finite \(W\)-algebras for general \(G\); they also recall the basic results parabolic quasi-map’s spaces and formulate its main conjecture. Thereafter, the authors recall the results of Brundan and Kleshchev who interpret finite \(W\)-algebras in type \(A\) using certain shifted Yangians and discuss the notion of Whittaker vectors for finite \(W\)-algebras from this point view. They use it in order to prove their main conjecture for \(G=GL(N)\) (and any parabolic). One important ingredient in the proof is this: they replace the intersection cohomology of parabolic quasi-map’s spaces by the ordinary cohomology of a small resolutions of those spaces. Finally, they discuss the relation between the above results and the AGT conjecture.