Representations of Lie Groups, Kyoto, Hiroshima, 1986

Characteristic Varieties of Highest Weight Modules and Primitive Quotients

Multiplicity One Theorems for Generalized Gelfand-Graev Representations of Semisimple Lie Groups and Whittaker Models for the Discrete Series

Lie Algebra Cohomology and Holomorphic Continuation of Generalized Jacquet Integrals

Certaines Répresentations Monomiales d'un Croupe de Lie Résoluble Exponentiel

Irreducibility of Discrete Series Representations for Semisimple Symmetric Spaces

A Classification Theory of Prehomogeneous Vector Spaces

Schur Orthogonality Relations for Non Square Integrable Representations of Real Semisimple Linear Group and Its Application

La Formule de Plancherei des Croupes de Lie Semi-Simples Réels

Some Remarks on Discrete Series Characters for Reductive p-adic Groups

Geometric Constructions of Representations

Character, Character Cycle, Fixed Point Theorem and Group Representations

A Survey of the Generalized Geroch Conjecture

Irreducible Unitary Representations of the Group of Maps with Values in a Free Product Group

Algebraic Structures on Virtual Characters of a Semisimple Lie Group

Cohomological Hardy Space for SU(2, 2)

Une Intégrale Invariante sur l'algèbre de Lie Symétrique Semi-Simple

Fundamental Groups of Semisimple Symmetric Spaces

A Description of Discrete Series for Semi-Simple Synunetric Spaces II

Closure Relations for Orbits on Affine Symmetric Spaces under the Action of Minimal Parabolic Subgroups

Asymptotic Behavior of Spherical Functions on Semisimple Symmetric Spaces

A Realization of Semisimple Symmetric Spaces and Construction of Boundary Value Maps

Boundedness of Certain Unitarizable Harish-Chandra Modules

Representations of Lie Groups, Kyoto, Hiroshima, 1986 contains the proceedings of a symposium on "Analysis on Homogeneous Spaces and Representations of Lie Groups" held on September 1-6, 1986 in Japan. The symposium provided a forum for discussing Lie groups and covered topics ranging from geometric constructions of representations to the irreducibility of discrete series representations for semisimple symmetric spaces. A classification theory of prehomogeneous vector spaces is also described.

Comprised of 22 chapters, this volume first considers the characteristic varieties of certain modules over the enveloping algebra of a semisimple Lie algebra, such as highest weight modules and primitive quotients. The reader is then introduced to multiplicity one theorems for generalized Gelfand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series. Subsequent chapters focus on Lie algebra cohomology and holomorphic continuation of generalized Jacquet integrals; the generalized Geroch conjecture; algebraic structures on virtual characters of a semisimple Lie group; and fundamental groups of semisimple symmetric spaces. The book concludes with an analysis of the boundedness of certain unitarizable Harish-Chandra modules.

This monograph will appeal to students, specialists, and researchers in the field of pure mathematics.