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Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits

Alice Barbara Tumpach — 2009

Annales de l’institut Fourier

In this paper, we construct a hyperkähler structure on the complexification $𝒪^{ℂ}$ of any Hermitian symmetric affine coadjoint orbit $𝒪$ of a semi-simple $L^{*}$ -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of $𝒪$ . By a relevant identification of the complex orbit $𝒪^{ℂ}$ with the cotangent space $T 𝒪$ of $𝒪$ induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on $T 𝒪$ compatible with...

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