Givental–PSZ quantum D-module comparison

Construct an isomorphism between the Givental and Pushkar–Smirnov–Zeitlin quantum D-modules for ADE quiver theories with dominant parameter, after extending both D-modules to the regular Kähler torus.

Background

The original quantum Hikita conjecture uses Givental’s quantum D-module, whereas the paper’s refinement uses the PSZ D-module. The two constructions are expected to agree over the regular Kähler torus in the good ADE setting, where the relevant equivariant and Kähler roots define the same arrangement.

The authors indicate that an adaptation of existing arguments may prove the statement, but it remains conjectural in the paper.

References

For $\Gamma$ of type ADE and dominant $\mu$, the $D$-modules $Q{\mathrm{Giv}$ and $Q{\mathrm{PSZ}$ extend to isomorphic $D$-modules on $\mathsf A{\mathrm{reg} \simeq {\mathsf{K}{\mathrm{reg}$.

— The quantum Hikita conjecture via quasimaps  (2608.16746 - Dinkins et al., 17 Aug 2026) in Conjecture 2.10, Section 2.7