Recently I have come across something I am not particularly familiar with, namely tensor invariants of $O(N)$, or isotropic tensors of $O(N)$ as I believe they are also called. What I would like to know are whether there exist any isotropic tensors of $O(N)$ that are not Kronecker deltas, Levi-Civita or a combinations of them both.
I have been looking at articles like https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0017089500006832 , and it says that it is true for $SO(N)$, i.e. $O(N)$ with determinant one. Unfortunately, this article only covers tensor invariants of $SO(N)$ and not the full $O(N)$.