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In this second volume of Bertram Kostant's collected papers, the reader will engage in Works published between 1967 and 1977. 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 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 is paper #36 for which Kostant was awarded the Steele Prize in 1990. Select commentaries and summaries of his papers conclude the volume.
List of contents
A Homomorphism in Exterior Algebra (with Novikoff, A.).- Quantization and Representation of Solvable Lie Groups (with Auslander, L.).- On Orbits Associated with Symmetric Spaces (with Rallis, S.).- On Representations Associated with Symmetric Spaces (with Rallis, S.).- On the Existence and Irreducibility of Certain Series of Representations.- On Certain Unitary Representations which arise from a Quantization Theory.- Orbits and Quantization Theory.- Quantization and Unitary Representations.- Orbits and Representations Associated with Symmetric Spaces (with Rallis, S.).- Polarization and Unitary Representations of Solvable Lie Groups (with Auslander, L.).- Line Bundles and the Prequantized Schrödinger Equation.- On Convexity, the Weyl Group and the Iwasawa Decomposition.- Symplectic Spinors.- Verma Modules and the Existence of Quasi-Invariant Differential Operators.- On the Existence and Irreducibility of Certain Series of Representations. On the Tensor Product of a Finite and an Infinite-Dimensional Representation.- On the Definition of Quantization.- The Euler Characteristic of an Affine Space Form is Zero (with Sullivan, D.).- On Macdonald's -Function Formula, the Laplacian and Generalized Exponents.- On the Structure of Certain Subalgebras of a Universal Enveloping Algebra (with Tirao, J.).- Graded Manifolds, Graded Lie Theory, and Prequantization.- Comments on Papers in Volume II.
About the author
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.
Summary
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.
