Collected Papers : Volume III 1978–1990

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.

Preface.- Acknowledgements.- On Whittaker Vectors and Representation Theory.- (with Kazhdan, D. and Sternberg, S.) Hamiltonian Group Actions and Dynamical Systems of Calogero Type.- Harmonic Analysis on Graded (or Super) Lie Groups.- The Solution to a Generalized Toda Lattice and Representation Theory.-  Quantization and Representation Theory.- A Lie Algebra Generalization of the Amitsur-Levitski Theorem.- Poisson Commutativity and Generalized Periodic Toda Lattice.- (with Sternberg, S.) Symplectic Projective Orbits.- Coadjoint Orbits and a New Symbol Calculus for Line Bundles.- The McKay Correspondence, The Coxeter Element and Representation Theory.- (with Kumar, S.) The Nil Hecke Ring and Cohomology of G/P for a Kac-Moody Group G.- (with Kumar, S.) The Nil Hecke Ring and Cohomology of G/P for a Kac-Moody Group G*.- (with Sternberg, S.) Symplectic Reduction, BRS Cohomology and Infinite-Dimensional Clifford Algebras.- (with Kumar, S.) T-Equivariant K-Theory of Generalized Flag Varieties.- (with Guillemin, V. and Sternberg, S.) Douglas'' Solution of the Plateau Problem.- The Principle of Triality and a Distinguished Unitary Representation of SO(4,4).- (with Sternberg, S.) The Schwartzian Derivative and the Conformal Geometry of the Lorentz Hyperboloid.- (with Kumar, S.) T-Equivariant K-Theory of Generalized Flag Varieties.- A Formula of Gauss-Kummer and the Trace of Certain Intertwining Operators.- The Vanishing of Scalar Curvature and the Minimal Representation of SO(4,4).- Comments on Papers in Volume III.