Resumen de Hard Lefschetz actions in Riemannian geometry with special holonomy
Naichung Conan Leung, Changzheng Li
It is known that the hard Lefschetz action, together with K\"ahler identities for K\"ahler (resp. hyperk\"ahler) manifolds, determines a $\mathfrak{su}(1,1)_{sup}$ (resp. $\mathfrak{sp}(1,1)_{sup}$) Lie superalgebra action on differential forms. In this paper, we explain the geometric origin of this action, and we also generalize it to manifolds with other holonomy groups. For semi-flat Calabi-Yau (resp. hyperk\"ahler) manifolds, these symmetries can be enlarged to a $\mathfrak{so}(2,2)_{sup}$ (resp. $\mathfrak{su}(2,2)_{sup}$) action.
