ArXived article on hyper-Kähler manifolds

By Jane Jamshidi, jaja@sdu.dk, 11/8/2021

Professor, Centre Director and D-IAS Chair  Jørgen Ellegaard Andersen has together with Alessandro Malusá from University of Toronto and  Gabriele Rembado from Hausdorff Centre for Mathematics at University of Bonn published new research on arXiv entitled: "Sp(1)-symmetric hyper-Kähler quantisation”.

In the article they provide a new general scheme for the geometric quantisation of Sp(1)-symmetric hyper-Kähler manifolds, considering Hilbert spaces of holomorphic sections over the associated twistor space. Under properness of an associated moment map, or other finiteness assumptions, they construct unitary quantum (super) representations of central extensions of certain subgroups of Riemannian isometries preserving the hyper-Kähler 2-sphere, and they study their decomposition in irreducible components. This quantisation scheme applies to hyper-Kähler vector spaces, the Taub-NUT metric on ℝ×𝕊3, moduli spaces of framed SU(r)-instantons on ℝ4, and moduli spaces of monopoles on ℝ3. 

Link to the paper on arXiv: https://arxiv.org/abs/2011.03584