Hikita surjectivity for $\mathcal{N}\mathrm{/}\mathrm{/}\mathrm{/}T$

The Hamiltonian reduction $\mathcal{N}\mathrm{/}\mathrm{/}\mathrm{/}T$ of the nilpotent cone in ${\mathfrak{s}\mathfrak{l}}_n$ by the torus of diagonal matrices is a Nakajima quiver variety which admits a symplectic resolution $\widetilde{\mathcal{N}\mathrm{/}\mathrm{/}\mathrm{/}T}$, and the corresponding BFN Coulomb branch is the affine closure $\overline{T^{\ast }(G\mathrm{/}U)}$ of the cotangent bundle of the base affine space. We construct a surjective map $\mathbb{C}\left[{\overline{T^{\ast }(G\mathrm{/}U)}}^{T\times B\mathrm{/}U}\right]\twoheadrightarrow H^{\ast }\left(\widetilde{\mathcal{N}\mathrm{/}\mathrm{/}\mathrm{/}T}\right)$ of graded algebras, which the Hikita conjecture predicts to be an isomorphism. Our map is inherited from a related case of the Hikita conjecture and factors through Kirwan surjectivity for quiver varieties. We conjecture that many other Hikita maps can be inherited from that of a related dual pair.