Diff\(_+(S^1)/S^1\) as a space of complex structures on loop spaces of compact Lie groups (Q2702421)

In the present paper the homogeneous Frechet space \(\text{Diff}_+(S^1)/S^1\) is realized as a space of complex structures on the loop space of a compact Lie group compatible with the symplectic structure. The basic results on the Kähler geometry of this model are collected in Section 2. In Section 3 the author defines a symplectic twistor bundle over the loop space of a compact Lie group, having \(\text{Diff}_+(S^1)/S^1\) as a fibre. Finally, a scheme for the twistor quantization of loop spaces of compact Lie groups is presented.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00049].