  We study the representation theory of the nested instantons quiver presented
in [1], which describes a particular class of surface defects in
four-dimensional supersymmetric gauge theories. We show that the moduli space
of its stable representations provides an ADHM-like construction for nested
Hilbert schemes of points on $\mathbb C^2$, for rank one, and for the moduli
space of flags of framed torsion-free sheaves on $\mathbb P^2$, for higher
rank. We introduce a natural torus action on this moduli space and use
equivariant localization to compute some of its (virtual) topological
invariants, including the case of compact toric surfaces. We conjecture that
the generating function of holomorphic Euler characteristics for rank one is
given in terms of polynomials in the equivariant weights, which, for specific
numerical types, coincide with (modified) Macdonald polynomials.
