Collected Papers

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.

• Whittaker vectors
• Representation theory
• Kostant collected papers
• Hamiltonian group actions
• Amitsur-Levitski theorem
• Poisson commutativity
• Toda lattice
• symplectic projective orbits
• McKay correspondence
• Nil Hecke ring
• T-Equivariant K-Theory
• Quantization and Representation Theory
• graded Lie groups
• super Lie groups

• Weizmann Institute of Science Fac. Mathematics & Computer Science, Rehovot, Israel

  Anthony Joseph

• University of North Carolina Dept. Mathematics, Chapel Hill, USA

  Shrawan Kumar

• Ecole Polytechnique Centre de Mathématiques, Palaiseau Cedex, France

  Michèle Vergne

• Dept. Mathematics, Massachusetts Institute of Technology (MIT), Cambridge, USA

  Bertram Kostant

​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.

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