Differential Invariants of Linear Symplectic Actions

TL;DR

This paper addresses the problem of classifying submanifolds and functions under symplectic and conformal symplectic group actions by computing differential invariants using the Lie-Tresse theorem.

Contribution

It provides a method to compute differential invariants for symplectic and conformal symplectic actions, advancing the understanding of their equivalence problem.

Findings

Computed differential invariants for symplectic actions

Solved the equivalence problem for symplectic and contact spaces

Applied Lie-Tresse theorem to linear symplectic actions

Abstract

We consider the equivalence problem for symplectic and conformal symplectic group actions on submanifolds and functions of symplectic and contact linear spaces. This is solved by computing differential invariants via the Lie-Tresse theorem.