Differential Geometry Seminar: Killing tensors on symmetric spaces

I will present some recent results on the structure of the algebra of Killing tensors on Riemannian symmetric spaces. The fundamental question is whether any Killing tensor field on a Riemannian symmetric space is a polynomial in (a symmetric product of) Killing vector fields.

For spaces of constant curvature, the answer is in the positive (as has been known for quite some time). The same is true for the complex projective space (Eastwood, 2023). Surprisingly, for other rank one symmetric spaces (quaternionic projective space and Cayley projective plane), the answer is almost always in the negative (Matveev-Nikolayevsky, 2024). If time permits we’ll also discuss the case of higher rank and some related results. This is a joint project with V. Matveev (University of Jena, Germany).

School of Computer and Mathematical Sciences