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 E 6, E 7, and E 8 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 E 6 E 7 and E 8 (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 Ï.- Clifford Algebra Analogue of the Hopf-Koszul-Samelson Theorem, the Ï -Decomposition, C (g)=End VÏ â C ( P ), and the g-Module Structure of â§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 â§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.