Differential invariants of the motion group actions

Abstract

Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the Lie-Tresse theorem, but may change a lot. We describe in details the case of the motion group O(n) ⋉ Rⁿ acting on the full (unconstraint) jet-space as well as on some invariant equations.