Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.Presents several different points of view on key topics in representation theory, from internationally known experts in the field

Lie groups. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Groups, Lie --- Group theory --- Lie algebras --- Symmetric spaces --- Topological groups --- Lie, Groupes de --- Lie, Algèbres de. --- Lie groups --- Representations of Lie groups --- Representations of Lie algebras --- Représentations de groupes de Lie. --- Représentations d'algèbres de Lie. --- Lie, Algèbres de. --- Représentations de groupes de Lie. --- Représentations d'algèbres de Lie.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Lie groups. --- Symmetric spaces. --- Topological Groups. --- Global differential geometry. --- Differential equations, partial. --- Harmonic analysis. --- Group theory. --- Topological Groups, Lie Groups. --- Differential Geometry. --- Several Complex Variables and Analytic Spaces. --- Abstract Harmonic Analysis. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Partial differential equations --- Geometry, Differential --- Groups, Topological --- Continuous groups --- Topological groups. --- Differential geometry. --- Functions of complex variables. --- Complex variables --- Elliptic functions --- Functions of real variables --- Differential geometry --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Group theory --- Differential geometry. Global analysis --- Topological groups. Lie groups --- Analytical spaces --- Mathematical analysis --- analyse (wiskunde) --- topologie (wiskunde) --- differentiaal geometrie --- wiskunde

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Group theory --- Differential geometry. Global analysis --- Topological groups. Lie groups --- Analytical spaces --- Mathematical analysis --- analyse (wiskunde) --- topologie (wiskunde) --- differentiaal geometrie --- wiskunde