Let M be a quaternionic-Kähler manifold, with fundamental form ω, and let L be the Lefschetz operator of ω. In the Kähler and, more generally, symplectic cases, there is a mysterious relation between the Lefschetz sl2-decomposition and the Hodge operator due to Weil (see Huybrechts 1.2.31)

Does there exist a quaternionic-Kähler analogue?

**Answer**

**Attribution***Source : Link , Question Author : Juan Corrida , Answer Author : Community*