Collected Papers: Volume IV 1991-2000

ISBN-13: 9780387095882 / Angielski / Twarda / 2022 / 644 str.

Shrawan Kumar

Opis

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. 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 fourth volume (1985-1995) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this fourth volume is Kostant's commentaries and summaries of his papers in his own words.

Spis treści

Preface.- Acknowledgements.- The Capelli Identity, Tube Domains, and the Generalized Laplace Transform (With Sahi, S.).- The Variety of all Invariant Symplectic Structures on a Homogeneous Space and Normalizers of Isotropy Subgroups (with Brylinski, R.).- A Geometric Realization of Minimal t-type of Harish-Chandra Modules for Complex S.S. Groups (with Kumar, S.).- Nilpotent Orbits, Normality, and Hamiltonian Group Actions (with Brylinski, R.).- The Vanishing of Scalar Curvature on 6 Manifolds, Einstein’s Equation, and Representation Theory.- Jordan Algebras and Capelli Identities (with Sahi, S.).-  Nilpotent Orbits, Normality, and Hamiltonian Group Actions (with Brylinski, R.).- Minimal Representations of E₆, E₇, and E₈ and the Generalized Capelli identity (with Brylinski, R.).- Groups and the Buckyball (with Chung, F.R.K. and Sternberg, S.).- Differential Operators on Conical Lagrangian Manifolds (with Brylinski, R.).- Minimal Representations, Geometric Quantization, and Unitarity (with Brylinski, R.).- Structure of the Truncated Icosahedron (such as Fullerene or Viral Coatings) and a 60-Element Conjugacy Class in PSl(2,11).- Immanant Inequalities and 0-Weight Spaces.- Lagrangian Models of Minimal Representations of E₆ E₇ and E₈ (with R. Brylinski).- Structure of the Truncated Icosahedron (e.g., Fullerene or C60, viral coatings) and a 60-Element Conjugacy Class in PSl(2,11).- The Graph of the Truncated Icosahedron and the Last Letter of Galois.- Flag Manifold Quantum Cohomology, the Toda Lattice, and the Representation with Highest Weight ρ.- Clifford Algebra Analogue of the Hopf–Koszul–Samelson Theorem, the ρ-Decomposition, C(g)=End V_ρ⊗C(P), and the g-Module Structure of ∧g.- Quantum Cohomology of the Flag Manifold as an Algebra of Rational Functions on a Unipotent Algebraic Group.- The Set of Abelian Ideals of a Borel Subalgebra, Cartan Decompositions, and Discrete Series Representations.- The Weyl Character Formula, the Half-Spin Representations, and Equal Rank Subgroups (with Gross, B., Ramond, P. and Sternberg, S.).- A Cubic Dirac Operator and the Emergence of Euler Number Multiplets of Representations for Equal Rank Subgroups.- On ∧g for a Semisimple Lie Algebra g, as an Equivariant Module over the Symmetric Algebra S(g).- A Generalization of the Bott–Borel–Weil Theorem and Euler Number Multiplets of Representations.- On Laguerre Polynomials, Bessel Functions, Hankel Transform and a Series in the Unitary Dual of the Simply-Connected Covering Group of Sl(2,R).- Comments on Papers in Volume IV.

O autorze

​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.

Blurb

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.

During his years as professor at the Masachusetts Institute of Technology from 1962 until retiring from teaching in 1993, he was elected to the National Academy of Sciences USA, the American Academy of Arts and Sciences, the AMS Steele Prize, Honorary Doctorates from University of Codoba, Argentina, the University of Salamanca, Spain, Purdue University. 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 fourth volume (1991-2000) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this fourth volume is Kostant's commentaries and summaries of his papers in his own words.