  If two conical symplectic resolutions $X\to X_0$ and $X^!\to X_0^!$ are
symplectic dual, the cohomology ring $H^*(X)$ and the coordinate ring of
$\mathbb{C}^*$-fixed points in $X_0^!$ are expected to be isomorphic as graded
algebras. This statement is called Hikita conjecture and it is known that the
conjecture holds for some cases. In this paper, we deal with the cohomology of
framed moduli spaces over the projective plane and the coordinate ring of
$\mathbb{C}^*$- fixed points of $\mathbb{C}^{2n}/((\mathbb{Z}/r\mathbb{Z})\wr
S_n) $ and show that these are isomorphic as graded vector spaces.
