Abstract
A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra đŁ. Under certain conditions, đŁ-invariant systems of differential equations are shown to be associated with đŁ-modules that are integrable with respect to some parabolic subalgebra of đŁ. The suggested construction is motivated by the unfolded formulation of dynamical equations developed in the higher spin gauge theory and provides a starting point for generalization to the nonlinear case. It is applied to the conformal algebra đŹ(M, 2) to classify all linear conformally invariant differential equations in the Minkowski space. Numerous examples of conformal equations are discussed from this perspective.
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