Causal Symmetric Spaces
This text is intended to introduce researchers and graduate students with a solid background in Lie theory to the concepts of causal symmetric spaces. The authors intend also to make the basic results and their proofs available and to describe some important lines of research in the field. To date, results of recent studies considered "standard" by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.
- Hardback | 250 pages
- 159 x 236 x 24mm | 667g
- 11 Sep 1996
- Elsevier Science Publishing Co Inc
- Academic Press Inc
- San Diego, United States
- b&w illustrations, references, bibliography, indexes
Table of contents
Symmetric spaces: basic structure theory, dual symmetric spaces, the module structure of q, a-subspaces, the hyperboloids. Causal orientations: covex cones and their auto-morphisms, causal orientations, semigroups, the order compactification, examples, symmetric spaces related to tube domains. Irreducible causal symmetric spaces: existence of causal structures, the classification of causal symmetric pairs. Classification of invariant cones: symmetric SL(2,R)-reduction, the minimal and maximal cones, the linear con-vexity theorem, the classification, extension of cones. The geometry: the bounded realisation of HHnK, the semigroup S(C), the causal intervals, compression semigroups, the non-linear convexity theorem, the B#-order, the affine closure of B#. The order compactification: causal galois connections, an alternative realisation of M+, the stabilisers for M+, theo orbit structure of M, the space SL(3,R)/SO(2,1). Holo-morphic representations: holomorphic representations of semi-groups, highest weight-modules, the holomorphic discrete series, classical hardy spaces, hardy spaces, the cauchy-szego kernel. Spherical functions: the classical laplace transform, spherical functions, the asymptotics, expansion formula, the spherical laplace transform, the abel transform, relation to representation theory. The wiener-hopf algebra.