Representations of Lie Groups, Kyoto, Hiroshima, 1986

K. Okamoto, T. Oshima

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780125251006
• eBook ISBN:
  9781483257570
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Table of contents

• Front Cover
• Representations of Lie Groups, Kyoto, Hiroshima, 1986
• Copyright Page
• Table of Contents
• Foreword
• Preface to the Present Volume
• Chapter 1. Characteristic Varieties of Highest Weight Modules and Primitive Quotients
• Chapter 2. Multiplicity One Theorems for Generalized Gelfand-Graev Representations of Semisimple Lie Groups and Whittaker Models for the Discrete Series
• Chapter 3. Lie Algebra Cohomology and Holomorphic Continuation of Generalized Jacquet Integrals
• Chapter 4. Certaines Représentations Monomiales d'un Groupe de Lie Résoluble Exponentiel
• Chapter 5. Irreducibility of Discrete Series Representations for Semisimple Symmetric Spaces
• Chapter 6. A Classification Theory of Prehomogeneous Vector Spaces
• Chapter 7. Schur Orthogonality Relations for Non Square Integrable Representations of Real Semisimple Linear Group and Its Application
• Chapter 8. La Formule de Plancherel des Groupes de Lie Semi-Simples Réels
• Chapter 9. Some Remarks on Discrete Series Characters for Reductive p-adic Groups
• Chapter 10. Geometric Constructions of Representations
• Chapter 11. Character, Character Cycle, Fixed Point Theorem and Group Representations
• Chapter 12. A Survey of the Generalized Geroch Conjecture
• Chapter 13. Irreducible Unitary Representations of the Group of Maps with Values in a Free Product Group
• Chapter 14. Algebraic Structures on Virtual Characters of a Semisimple Lie Group
• Chapter 15. Cohomological Hardy Space for SU(2, 2)
• Chapter 16. Une Intégrale Invariante sur l'algébre de Lie Symétrique Semi-Simple
• Chapter 17. Fundamental Groups of Semisimple Symmetric Spaces
• Chapter 18. A Description of Discrete Series for Semisimple Symmetric Spaces II
• Chapter 19. Closure Relations for Orbits on Affine Symmetric Spaces under the Action of Minimal Parabolic Subgroups
• Chapter 20. Asymptotic Behavior of Spherical Functions on Semisimple Symmetric Spaces
• Chapter 21. A Realization of Semisimple Symmetric Spaces and Construction of Boundary Value Maps
• Chapter 22. Boundedness of Certain Unitarizable Harish-Chandra Modules