  Let $M^K_n$ be the moduli space of framed $K$-instantons with instanton
number $n$ when $K$ is a compact simple Lie group of classical type. Due to
Donaldson's theorem, its scheme structure is given by the regular locus of a
GIT quotient of $\mu^{-1}(0)$ where $\mu$ is the moment map on the associated
symplectic vector space of ADHM data.
  A main theorem of this paper asserts that $\mu$ is flat for
$K=SO(3,\mathbb{R})$ and any $n\ge0$. Hence we complete the interpretation of
the K-theoretic Nekrasov partition function for the classical groups in
Nekrasov-Shadchin's work in term of Hilbert series of the instanton moduli
spaces together with the author's previous results.
  We also write ADHM data for the second symmetric and exterior products of the
associated vector bundle of an instanton. This gives an explicit
quiver-theoretic description of the isomorphism $M^{K}_{n}\cong M^{K'}_{n}$ for
all the pairs $K,K'$ with isomorphic Lie algebras.
