Title | Infinite Dimensional Kรคhler Manifolds [electronic resource] / edited by Alan Huckleberry, Tilmann Wurzbacher |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8227-9 |
Descript | XIII, 375 p. online resource |
to Group Actions in Symplectic and Complex Geometry -- I. Finite-dimensional manifolds -- II. Elements of Lie groups and their actions -- III. Manifolds with additional structure -- IV. Symplectic manifolds with symmetry -- V. Kรคhlerian structures on coadjoint orbits of compact groups and associated representations -- Literature -- Infinite-dimensional Groups and their Representations -- I. Calculus in locally convex spaces -- II. Dual spaces of locally convex spaces -- III. Topologies on function spaces -- IV. Representations of infinite-dimensional groups -- V. Generalized coherent state representations -- References -- Borel-Weil Theory for Loop Groups -- I. Compact groups -- II. Loop groups and their central extensions -- III. Root decompositions -- IV. Representations of loop groups -- V. Representations of involutive semigroups -- VI. Borel-Weil theory -- VII. Consequences for general representations -- References -- Coadjoint Representation of Virasoro-type Lie Algebras and Differential Operators on Tensor-densities -- I. Coadjoint representation of Virasoro group and Sturm-Liouville operators; Schwarzian derivative as a 1-cocycle -- II. Projectively invariant version of the Gelfand-Fuchs cocycle and of the Schwarzian derivative -- III. Kirillovโs method of Lie superalgebras -- IV. Invariants of coadjoint representation of the Virasoro group -- V. Extension of the Lie algebra of first order linear differential operators on S1 and matrix analogue of the Sturm-Liouville operator -- VI. Geometrical definition of the Gelfand-Dickey bracket and the relation to the Moyal-Weil star-product -- References -- From Group Actions to Determinant Bundles Using (Heat-kernel) Renormalization Techniques -- I. Renormalization techniques -- II. The first Chern form on a class of hermitian vector bundles -- III. The geometry of gauge orbits -- IV. The geometry of determinant bundles -- V. An example: the action of diffeomorphisms on complex structures -- References -- Fermionic Second Quantization and the Geometry of the Restricted Grassmannian -- I. Fermionic second quantization -- II. Bogoliubov transformations and the Schwinger term -- III. The restricted Grassmannian of a polarized Hilbert space -- IV. The non-equivariant moment map of the restricted Grassmannian -- V. The determinant line bundle on the restricted Grassmannian -- References