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On invariants and equivalence of differential operators under Lie pseudogroups actions (2302.07833v1)
Published 2 Feb 2023 in math.DG, math-ph, and math.MP
Abstract: In this paper, we study invariants of linear differential operators with respect to algebraic Lie pseudogroups. Then we use these invariants and the principle of n-invariants to get normal forms (or models) of the differential operators and solve the equivalence problem for actions of algebraic Lie pseudogroups. As a running example of application of the methods, we use the pseudogroup of local symplectomorphisms.