Ebook: Collected Papers: Volume I 1955-1966

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.

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.

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Content:
Front Matter....Pages i-xix
Holonomy and the Lie Algebra of Infinitesimal Motions of A Riemannian Manifold....Pages 1-15
On the Conjugacy of Real Cartan Subalgebras....Pages 16-19
On the Conjugacy of Real Cartan Subalgebras II....Pages 20-27
On INV Ariant Skew-Tensors....Pages 28-31
On Differential Geomentry and Homogeneous Spaces. I.....Pages 32-35
On Differential Geometry and Homogeneous Spaces II....Pages 36-39
On Holonomy and Homogeneous Spaces....Pages 40-63
A Theorem of Frobenius, a Theorem of Amitsur-Levitski and Cohomology Theory....Pages 64-91
A Characterization of the Classical Groups....Pages 92-108
A Formula for the Multiplicity of a Weight....Pages 109-129
The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group....Pages 130-189
A Characterization of Invariant Affine Connections....Pages 190-205
Lie Algebra Cohomology and the Generalized Borel-Weil Theorem....Pages 206-264
Differential Forms on Regular Affine Algebras....Pages 265-290
Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups....Pages 291-308
Lie Group Representations On Polynomial Rings....Pages 309-317
Lie Group Representations on Polynomial Rings....Pages 318-395
Lie Algebra Cohomology and Generalized Schubert Cells....Pages 396-468
Eigenvalues of a Laplacian and Commutative Lie Subalgebras....Pages 469-481
Orbits, Symplectic Structures and Representation Theory....Pages 482-482
Back Matter....Pages 483-491
....Pages 1-26