Department of Mathematics and Statistics,

Dalhousie University,

Halifax, Nova Scotia, B3H 3J5

CANADA

E-mail: Roman.Smirnov@Dal.Ca

**Generalized Killing tensors: At the confluence of Differential
Geometry, Invariant Theory, Mathematical Physics and Representation Theory**

**Abstract:**

I will review the main results obtained in the course of the last 15
years in the study of (generalized) Killing tensors with the emphasis on
their relevance in various areas of mathematics and mathematical physics.

**References** (see also the relevant references therein)

- M. Eastwood, Representations via overdetermined systems, to appear in Contemp. Math. (2004).
- J.T. Horwood, R.G. McLenaghan and R.G. Smirnov, Invariant classification of orthogonal separable Hamiltonian systems in Euclidean space, to appear in Comm. Math. Phys. (2005).
- E.G. Kalnins, J.M. Kress and W. Miller, Jr. Second order superintegrable systems in conformally flat spaces I. 2D classical structure theory, to appear in J. Math. Phys. (2005).
- A.G. Nikitin and A.I. Prilipko, Generalized Killing tensors and the symmetry of the Klein-Gordon-Fock equation, preprint-90.23, Acad. Sci. Ukr.SSR., Institute of Mathematics, Kiev, 1990, 59 pages.
- P.J. Olver, Classical Invariant Theory, London Mathematical Society, Student Texts 44, (Cambridge University Press, 1999).