Loop groups. Repr. with corrections. (English) Zbl 0638.22009

Pressley, Andrew; Segal, Graeme

Oxford Mathematical Monographs. Oxford (UK): Clarendon Press. viii, 318 p. £15.00 (1988).

See the extensive review by S. I. Gel’fand in Zbl 0618.22011 of the first edition (1986).

MSC:

22E65	Infinite-dimensional Lie groups and their Lie algebras: general properties
17B67	Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
22-02	Research exposition (monographs, survey articles) pertaining to topological groups
46M20	Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
14M15	Grassmannians, Schubert varieties, flag manifolds
43A85	Harmonic analysis on homogeneous spaces
32M10	Homogeneous complex manifolds

Keywords:

determinant line bundle; vertex operators; loop group; Kac-Moody Lie algebras; affine algebras; infinite-dimensional Lie groups; central extensions; circle group; Grassmannian; polarized Hilbert space; Schubert cell decomposition; homogeneous space; complex manifold; Borel-Weil theory; spin representation; Kac character formula; Bernstein-Gel’fand- Gel’fand resolution

Citations:

Zbl 0549.00013; Zbl 0618.22011