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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. 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 fifthvolume (2001-2015) of a five-volume set of Bertram Kostant's collected papers.
List of contents
The Weyl algebra and the structure of all Lie superalgebras of Riemannian type.- Dirac cohomology for the cubic Dirac operator.- The generalized Cayley map from an algebraic group to its Lie algebra.- A branching law for subgroups fixed by an involution and a noncompact analogue of the Borel-Weil theorem.- Powers of the Euler product and commutative subalgebras of a complex simple Lie algebra.- Minimal coadjoint orbits and symplectic induction.- The Coxeter element and the branching law for the finite subgroup of SU(2).- Gelfand-Zeitlin theory from the perspective of classical mechanics. I.- Gelfand-Zeitlin theory from the perspective of classical mechanics. II.- On the centralizer of K in U(g).- Fomenko-Mischenko theory, Hessenberg varieties, and polarizations.- Root systems for Levi factors and Borel-de Siebenthal theory.- On a theorem of Ranee Brylinski.- Experimental evidence for the occurrence of E8 in nature and the radii of the Gosset circles.- On some exotic finite subgroups of E8 and Springer's regular elements of the Weyl group.- On the algebraic set of singular elements in a complex simple Lie algebra.- The cascade of orthogonal roots and the coadjoint structure of the nilradical of a Borel subgroup of a semisimple Lie group.- Center U(n), Cascade of orthogonal roots, and a construction of Lipsman-Wolf.- Action of the conformal group on steady state solutions to Maxwell's equations and background radiation.- Equations for a filtration of sheets and the variety of singular elements of a complex semisimple Lie algebra
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
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. 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 fifthvolume (2001-2015) of a five-volume set of Bertram Kostant's collected papers.
