The adapted hyper-K\"ahler structure on the crown domain

Laura Geatti; Andrea Iannuzzi

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arXiv · 1711.01605

The adapted hyper-K\"ahler structure on the crown domain

Laura Geatti·Andrea Iannuzzi

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Abstract

Let $\,\Xi\,$ be the crown domain associated with a non-compact irreducible hermitian symmetric space $\,G/K$. We give an explicit description of the unique $\,G$-invariant adapted hyper-K\"ahler structure on $\,\Xi$,$\ $i.$\,$e.$\ $compatible with the adapted complex structure $\,J_{ad}\,$ and with the $\,G$-invariant K\"ahler structure of $\,G/K$. We also compute invariant potentials of the involved K\"ahler metrics and the associated moment maps.

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Laura Geatti, Andrea Iannuzzi. 2017-11-05. The adapted hyper-K\"ahler structure on the crown domain. https://arxiv.org/abs/1711.01605

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