Title of lectures
Integrable systems, symmetries and Lie algebra contractions
Lecturer:
Pavel WINTERNITZ, Université de Montréal
Outline:
Lecture 1. Finite dimensional integrable classical and quantum systems with
overcomplete sets of commuting integrals of motion.
Relation to the separation of variables in Hamilton-Jacobi and Schrodinger
equations.
Lecture 2. Lie algebra contractions and separation of variables.
Tree diagrams aand subgroup diagrams for rotation groups and Euclidean
groups.
Lecture 3. Symmetry methods for differential and difference equations.
Linear equations and commuting sets of differential or difference
operators. Symmetries of nonlinear integrable difference equations
References:
[1] Miller, W., Jr., Symmetry and Separation of Variables, Addison-Wesley,
Reading, MA, 1977.
[2] Winternitz, P., Lie groups and solutions of nonlinear partial differential
equations, in: Integrable Systems, Quantum Groups and Quantum Field Theories,
Kluwer, Dordrecht, 1993.
[3] Olver, P.J., Applications of Lie Groups to Differential Equations,
Springer, New York,1993.
[4] Izmest'ev, A.A., Pogosyan, G.S., Sissakian, A.N., and Winternitz, P.,
Contractions of Lie algebras and the separation of variables, J. Math. Phys .
40 (1999) 1549-1573.
Lecture