DT-GV correspondence on the Mukai-Umemura variety

We compute Donaldson-Thomas(DT) invariants and their descendant invariants for the local Calabi-Yau 4-fold over the Mukai-Umemura variety via several localization formulas. Assuming that the genus-one Gopakumar-Vafa(GV) type invariants vanish, our computations verify the predictions of Cao, Maulik, and Toda.