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Spin Structures for Quaternionic-Kaehler and Hyper-Kaehler Manifolds

A very natural Dirac operator for Wolf spaces is discussed in Köhler, K, Weingart, G., Quaternionic analytic torsion, Adv. Math. 178 (2003), 375–395. It acts on subcomplexes of the de Rham complex, in …
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Homogeneous Quaternionic-Kähler Structure of the Grassmannians?

These spaces are Wolf spaces of the form $G/K$, where $K$ or a double cover equals $H\times SU(2)$. Here, $G=SU(p+2)$ and $H=U(p)$. The isotropy representation here is the exterior tensor product of s …
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