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Summary
Table of Contents
Preface | |
Introduction to Group Actions in Symplectic and Complex Geometry | |
Finite-dimensional manifolds | p. 1 |
Element of Lie groups and their actions | p. 20 |
Manifolds with additional structure | p. 40 |
Symplectic manifolds with symmetry | p. 82 |
Kahlerian structures on coadjoint orbits of compact groups and associated representations | p. 95 |
Infinite-dimensional Groups and their Representations | |
Calculus in locally convex spaces | p. 132 |
Dual spaces of locally convex spaces | p. 144 |
Topologies on function spaces | p. 153 |
Representations of infinite-dimensional groups | p. 164 |
Generalized coherent state representations | p. 168 |
Borel-Weil Theory for Loop Groups | |
Compact groups | p. 180 |
Loop groups and their central extensions | p. 181 |
Root decompositions | p. 197 |
Representations of loop groups | p. 201 |
Representations of involutive semigroups | p. 209 |
Borel-Weil theory | p. 213 |
Consequences for general representations | p. 226 |
Coadjoint Representation of Virasoro-type Lie Algebras and Differential Operators on Tensor-densities | |
Coadjoint representation of Virasoro group and Sturm-Liouville operators; Schwarzian derivative as a 1-cocycle | p. 233 |
Projectively invariant version of the Gelfand-Fuchs cocycle and of the Schwarzian derivative | p. 238 |
Kirillov's method of Lie superalgebras | p. 241 |
Invariants of coadjoint representation of the Virasoro group | p. 244 |
Extension of the Lie algebra of first order linear differential operators on S[superscript 1] and matrix analogue of the Sturm-Liouville operator | p. 247 |
Geometrical definition of the Gelfand-Dickey bracket and the relation to the Moyal-Weil star-product | p. 249 |
From Group Actions to Determinant Bundles Using (Heat-kernel) Renormalization Techniques | |
Renormalization techniques | p. 260 |
The first Chern form on a class of hermitian vector bundles | p. 266 |
The geometry of gauge orbits | p. 270 |
The geometry of determinant bundles | p. 275 |
An example: the action of diffeomorphisms on complex structures | p. 278 |
Fermionic Second Quantization and the Geometry of the Restricted Grassmannian | |
Fermionic second quantization | p. 290 |
Bogoliubov transformations and the Schwinger term | p. 298 |
The restricted Grassmannian of a polarized Hilbert space | p. 326 |
The non-equivariant moment map of the restricted Grassmannian | p. 336 |
The determinant line bundle on the restricted Grassmannian | p. 358 |
Table of Contents provided by Blackwell. All Rights Reserved. |
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