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.
Mục lục
Holonomy and the Lie Algebra of Infinitesimal Motions of A Riemannian Manifold.- On the Conjugacy of Real Cartan Subalgebras.- On the Conjugacy of Real Cartan Subalgebras II.- On INV Ariant Skew-Tensors.- On Differential Geomentry and Homogeneous Spaces. I..- On Differential Geometry and Homogeneous Spaces II.- On Holonomy and Homogeneous Spaces.- A Theorem of Frobenius, a Theorem of Amitsur-Levitski and Cohomology Theory.- A Characterization of the Classical Groups.- A Formula for the Multiplicity of a Weight.- The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group.- A Characterization of Invariant Affine Connections.- Lie Algebra Cohomology and the Generalized Borel-Weil Theorem.- Differential Forms on Regular Affine Algebras.- Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups.- Lie Group Representations On Polynomial Rings.- Lie Group Representations on Polynomial Rings.- Lie Algebra Cohomology and Generalized Schubert Cells.- Eigenvalues of a Laplacian and Commutative Lie Subalgebras.- Orbits, Symplectic Structures and Representation Theory.- Groups Over.
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