Symmetries and Overdetermined Systems of Partial Differential Equations (The IMA Volumes in Mathematics and its Applications)

Front Matter....Pages i-xv
Front Matter....Pages xvi-xvi
Overdetermined Systems, Conformal Differential Geometry, and the BGG Complex....Pages 1-24
Generalized Wilczynski Invariants for Non-Linear Ordinary Differential Equations....Pages 25-40
Notes on Projective Differential Geometry....Pages 41-60
Ambient Metric Construction of CR Invariant Differential Operators....Pages 61-75
Fine Structure for Second Order Superintegrable Systems....Pages 77-103
Differential Geometry of Submanifolds of Projective Space....Pages 105-125
Pseudo-Groups, Moving Frames, and Differential Invariants....Pages 127-149
Geometry of Linear Differential Systems Towards Contact Geometry of Second Order....Pages 151-203
Front Matter....Pages 204-204
On Geometric Properties of Joint Invariants of Killing Tensors....Pages 205-221
Hamiltonian Curve Flows in lie Groups G ⊂ U(N) and Vector Nls, mKdV, Sine-Gordon Soliton Equations....Pages 223-250
Conformal Killing Spinors and the Holonomy Problem in Lorentzian Geometry — A Survey of New Results —....Pages 251-264
Projective-Type Differential Invariants for Curves and Their Associated Pdes of Kdv Type....Pages 265-275
Algebraic Construction of the Quadratic First Integrals for a Special Class of Orthogonal Separable Systems....Pages 277-304
Geometry of Non-Regular Separation....Pages 305-317
Higher Symmetries of the Square of the Laplacian....Pages 319-338
Metric Connections in Projective Differential Geometry....Pages 339-350
Exterior Differential Systems with Symmetry....Pages 351-366
Partially Invariant Solutions to Ideal Magnetohydrodynamics....Pages 367-381
Invariant Prolongation and Detour Complexes....Pages 383-401
Inhomogeneous Ambient Metrics....Pages 403-420
Front Matter....Pages 204-204
Pfaffian Systems Of Frobenius Type And Solvability Of Generic Overdetermined Pde Systems....Pages 421-429
Exact And Quasi — Exact Solvability of Second Order Superintegrable Quantum Systems....Pages 431-444
A Remark On Unitary Conformal Holonomy....Pages 445-460
Polynomial Associative Algebras for Quantum Superintegrable Systems with a Third Order Integral of Motion....Pages 461-469
Separation of Variables for Systems of First-Order Partial Differential Equations and the Dirac Equation in Two-Dimensional Manifolds....Pages 471-496
Differential Systems Associated with Tableaux over Lie Algebras....Pages 497-513
Conformal Structures with Explicit Ambient Metrics and Conformal G 2 Holonomy....Pages 515-526
Deformations of Quadratic Algebras, the Joseph Ideal for Classical Lie Algebras, and Special Tensors....Pages 527-536
Analogues of the Dolbeault Complex and the Separation of Variables....Pages 537-550
Back Matter....Pages 551-563