Collected Papers

Hauptbeschreibung

In this third volume of Bertram Kostant's collected papers, the reader will engage in Works published between 1978 and 1990 of one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. Some specific topics cover algebraic groups and invariant theory, the geometry of homogeneous spaces, representation theory, geometric quantization and symplectic geometry, Lie algebra cohomology, Hamiltonian mechanics, modular forms, Whittaker theory, Toda lattice, and much more. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. A distinguished feature of this second volume are Kostant's commentaries  and summaries of his papers in his own words in addition to commentaries from colleagues.

Klappentext

In this third volume of Bertram Kostant's collected papers, the reader will engage in Works published between 1978 and 1990 of one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. Some specific topics cover algebraic groups and invariant theory, the geometry of homogeneous spaces, representation theory, geometric quantization and symplectic geometry, Lie algebra cohomology, Hamiltonian mechanics, modular forms, Whittaker theory, Toda lattice, and much more. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. A distinguished feature of this second volume are Kostant's commentaries  and summaries of his papers in his own words in addition to commentaries from colleagues.

Inhaltsverzeichnis

Preface.- Acknowledgements.- On Whittaker Vectors and Representation Theory.- (with Kazhdan, D. and Sternberg, S.) Hamiltonian Group Actions and Dynamical Systems of Calogero Type.- Harmonic Analysis on Graded (or Super) Lie Groups.- The Solution to a Generalized Toda Lattice and Representation Theory.-  Quantization and Representation Theory.- A Lie Algebra Generalization of the Amitsur–Levitski Theorem.- Poisson Commutativity and Generalized Periodic Toda Lattice.- (with Sternberg, S.) Symplectic Projective Orbits.- Coadjoint Orbits and a New Symbol Calculus for Line Bundles.- The McKay Correspondence, The Coxeter Element and Representation Theory.- (with Kumar, S.) The Nil Hecke Ring and Cohomology of
G
/
P
for a Kac–Moody Group
G
.- (with Kumar, S.) The Nil Hecke Ring and Cohomology of
G
/
P
for a Kac–Moody Group
G
*.- (with Sternberg, S.) Symplectic Reduction, BRS Cohomology and Infinite-Dimensional Clifford Algebras.- (with Kumar, S.)
T
-Equivariant
K
-Theory of Generalized Flag Varieties.- (with Guillemin, V. and Sternberg, S.) Douglas’ Solution of the Plateau Problem.- The Principle of Triality and a Distinguished Unitary Representation of SO(4,4).- (with Sternberg, S.) The Schwartzian Derivative and the Conformal Geometry of the Lorentz Hyperboloid.- (with Kumar, S.)
T
-Equivariant
K
-Theory of Generalized Flag Varieties.- A Formula of Gauss–Kummer and the Trace of Certain Intertwining Operators.- The Vanishing of Scalar Curvature and the Minimal Representation of SO(4,4).- Comments on Papers in Volume III.

Biografische Anmerkung zu den Verfassern

Bertram Kostant
was Professor Emeritus at MIT. He died on February 2, 2017 at 88 years old. Kostant was of one of the major architects of modern Lie theory and virtually all of his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests spanned a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. He also had a long standing love affair with the icosahedron. Bertram Kostant was elected to the National Academy of Sciences in 1978, became a Sackler Institute Fellow at Tel Aviv University in 1982, received a medal from the College de France in 1983. In 2012 he became a Fellow of the American Mathematical Society. He was awarded the Steele Prize in 1990 for his paper On the existence and irreducibility of certain series of representations; paper #36 in Volume II of Kostant’s Collected Papers. In 2016 he received the Wigner Medal in Rio de Janeiro. During his mathematical career, Kostant received several honorary doctorates.

• Whittaker vectors
• Representation theory
• Kostant collected papers
• Hamiltonian group actions
• Amitsur-Levitski theorem
• Poisson commutativity
• Toda lattice
• symplectic projective orbits
• McKay correspondence
• Nil Hecke ring
• T-Equivariant K-Theory
• Quantization and Representation Theory
• graded Lie groups
• super Lie groups