Noncompact Semisimple Lie Algebras and Groups

With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory supplemented by many concrete examples for a great variety of noncompact semisimple Lie algebras and groups.

Contents:

Introduction

Lie Algebras and Groups

Real Semisimple Lie Algebras

Invariant Differential Operators

Case of the Anti-de Sitter Group

Conformal Case in 4D

Kazhdan–Lusztig Polynomials, Subsingular Vectors, and Conditionally Invariant Equations

Invariant Differential Operators for Noncompact Lie Algebras Parabolically Related to Conformal Lie Algebras

Multilinear Invariant Differential Operators from New Generalized Verma Modules

Bibliography

Author Index

Subject Index