Lie Theory
Unitary Representations and Compactifications of Symmetric Spaces
Anker, Jean-Philippe.
editor.
Orsted, Bent.
editor.
SpringerLink (Online service)
text
xxu
2005
monographic
eng
access
X, 207 p. 20 illus. online resource.
Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A. Borel, L. Ji, and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles. Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups and symmetric spaces is required of the reader.
to Symmetric Spaces and Their Compactifications -- Compactifications of Symmetric and Locally Symmetric Spaces -- Restrictions of Unitary Representations of Real Reductive Groups.
edited by Jean-Philippe Anker, Bent Orsted.
Mathematics
Group theory
Topological groups
Lie groups
Harmonic analysis
Functions of complex variables
Differential geometry
Mathematics
Topological Groups, Lie Groups
Differential Geometry
Several Complex Variables and Analytic Spaces
Abstract Harmonic Analysis
Group Theory and Generalizations
QA252.3
QA387
512.55
512.482
Springer eBooks
Progress in Mathematics ; 229
9780817644307
http://dx.doi.org/10.1007/b139076
http://dx.doi.org/10.1007/b139076
100301
20180115171431.0
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