TY - BOOK
AU - Anker,Jean-Philippe
AU - Orsted,Bent
ED - SpringerLink (Online service)
TI - Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces
T2 - Progress in Mathematics
SN - 9780817644307
AV - QA252.3
U1 - 512.55 23
PY - 2005///
CY - Boston, MA
PB - Birkhäuser Boston
KW - Mathematics
KW - Group theory
KW - Topological groups
KW - Lie groups
KW - Harmonic analysis
KW - Functions of complex variables
KW - Differential geometry
KW - Topological Groups, Lie Groups
KW - Differential Geometry
KW - Several Complex Variables and Analytic Spaces
KW - Abstract Harmonic Analysis
KW - Group Theory and Generalizations
N1 - to Symmetric Spaces and Their Compactifications -- Compactifications of Symmetric and Locally Symmetric Spaces -- Restrictions of Unitary Representations of Real Reductive Groups
N2 - 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
UR - http://dx.doi.org/10.1007/b139076
ER -