Affine Laumon Spaces and Iterated $${\mathcal W}$$-Algebras

A family of vertex algebras whose universal Verma modules coincide with the cohomology affine Laumon spaces is found. This result based on an explicit expression for generating function Poincaré polynomials these spaces. There a variant quantum Hamiltonian reduction that realizes which we call iterated $${\mathcal W}$$ -algebras and our main conjecture associated to are subalgebras -algebras.