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

The cohomology of framed moduli spaces and the coordinate ring of torus fixed points of quotient singularities