Synopses & Reviews
This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant's fundamental work in all these areas has provided deep new insights and connections, and has created new fields of research. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Kostant's work.
"[The papers] are of high interest and high quality and make this volume one of the most interesting and coherent collective publications this reviewer has ever seen." -Int. Math. Nach.
This volume is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Bertram Kostant's work.
Table of Contents
Preface.-Normality of Some Nilpotent Varieties and Cohomology of Line Bundles on the Cotangent Bundle of the Flag Variety.-Holomorphic Quantization and Unitary Representations of the Tecichmüller Group.-Differential Operators on Conical Lagrangian Manifolds.-Groups and Buckyball.-Spinor and Oscillator Representations of Quantum Groups.-Famillles Cohérentes sur les Groupes de Lie Semi-simples et Restriction aux Sous-groupes Compacts Maximaux.-The Differntail Geometry of Fedosov's Quantization.-Closedness of Star Products and Cohomologies.-The Algebra of Chern-Simons Classes, the Poisson Bracket on it and the Action of the Gauge Group.-A Distinguished Family of Unitary Representations for the Exceptional Groups of Real Rank = 4.-Reduced Phase spaces and Riemann-Roch.-The Invariants of Degree up to 6 of all n-ary m-ics.-Tensor Products of Modules for a Vertex Operator Algebra and Vertex Tensor Categories.-Enveloping Algebras: Problems Old and New.-Integrable Highest Weight Modules Over Affine Superalgebras and Number Theory.-Quasi-Equivariant D-Modules, Equivariant Derived Category, and Representations of Reductive Lie Groups.-Meromorphic Monidal Structures.-The Nil Hecke Ring and Singularity of Schubert Varieties.-Some Classical and Quantum Algebras.-Total Positivity in Reductive Groups.-The Spectrum of Certain Invariant Differential Operators Associated to a Hermitian Symmetric Space.-Compact Subvarieties in Flag Domains.