String quantization on group manifolds and the holomorphic geometry of Diff \(S^ 1/S^ 1\) (Q1093970)

The recent results by Bowick and Rajeev on the relation of the geometry of Diff \(S^ 1/S^ 1\) and string quantization in \({\mathbb{R}}^{d,1}\) are extended to a string moving on a group manifold. A new derivation of the curvature formula \((-(26/12)m^ 3+(1/6)m)\delta_{n,-m}\) for the canonical holomorphic line bundle over Diff \(S^ 1/S^ 1\) is given which clarifies the relation of that bundle with the complex line bundles over infinite-dimensional Grassmannians, studied by Pressley and Segal.