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Collected Papers: Volume III 1978–1990

Autor Bertram Kostant Editat de Anthony Joseph, Shrawan Kumar, Michèle Vergne
en Limba Engleză Hardback – 2 dec 2022
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.

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Specificații

ISBN-13: 9780387095868
ISBN-10: 0387095861
Pagini: 644
Ilustrații: XIX, 703 p. 43 illus.
Dimensiuni: 178 x 254 mm
Greutate: 1.54 kg
Ediția:1st ed. 2023
Editura: Springer
Colecția Springer
Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

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.

Notă biografică

​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.

Textul de pe ultima copertă

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.


Caracteristici

Kostant is an architect of modern Lie theory and his mathematics interests span a huge range Kostant's papers reach deep results, giving rise to whole new fields of activities Kostant has been honored by numerous prestigious organizations over the six decades of his career

Descriere

Descriere de la o altă ediție sau format:
For more than five decades Bertram Kostant has been 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.
During his years as professor at the Massachusetts Institute of Technology from 1962 until retiring from teaching in 1993, he received many honors and prizes:  election to the National Academy of Sciences USA, the American Academy of Arts and Sciences, the AMS Steele Prize, Honorary Doctorates from University of Córdoba, Argentina, the University of Salamanca, Spain, Purdue University. 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.
This is the first volume (1955-1966) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this first volume is Kostant's commentaries and summaries of his papers in his own words.