The adapted hyper-Kähler structure on the crown domain (Q1729734)

The authors consider a non-compact Hermitian symmetric space $G/K$ and the crown domain $\Xi$ associated with $G/K$. They show that $\Xi$ admits a unique $G$-invariant adapted hyper-Kähler structure by formulating all quantities explicitly using Lie theory. The adapted hyper-Kähler structure is compatible with the adapted complex structure and with the $G$-invariant Kähler structure of $G/K$. Similarly, the authors compute the invariant potentials of the Kähler metrics and the associated moment maps.