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:IntroductionLie Algebras and GroupsReal Semisimple Lie
AlgebrasInvariant Differential OperatorsCase of the Anti-de Sitter GroupConformal Case in
4DKazhdan Lusztig Polynomials Subsingular Vectors and Conditionally Invariant
EquationsInvariant Differential Operators for Noncompact Lie Algebras Parabolically Related to
Conformal Lie AlgebrasMultilinear Invariant Differential Operators from New Generalized Verma
ModulesBibliographyAuthor IndexSubject Index
