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"We study conformal symmetry breaking differential operators which map differential forms on Rn to differential forms on a codimension one subspace Rn-1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn-1. They correspond to homomorphisms of generalized Verma modules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F-method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the related branching problems restricting generalized Verma modules for so(n+1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking differential operators in terms of the first-order operators d, δ, d and δ and certain hypergeometric polynomials. A dominant role in these studies is played by two infinite sequences of symmetry breaking differential operators which depend on a complex parameter λ. Their values at special values of λ appear as factors in two systems of factorization identities which involve the Branson-Gover operators of the Euclidean metrics on Rn and Rn-1 and the operators d, δ, d and δ as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn-1, respectively"--

Differential operators. --- Conformal geometry. --- Symmetry (Mathematics) --- Opérateurs différentiels --- Géométrie conforme --- Symétrie

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Stochastic differential equations. --- Differential operators. --- Equations différentielles stochastiques --- Opérateurs différentiels --- Stochastic differential equations --- Differential operators --- Equations différentielles stochastiques --- Opérateurs différentiels

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Quantum theory --- Schrödinger operator --- Spectral theory (Mathematics) --- Partial differential operators --- Théorie quantique. --- Schrödinger, Opérateur de. --- Théorie spectrale (mathématiques) --- Opérateurs différentiels partiels.

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Algebra --- Differential operators. --- Invariants. --- Index theory (Mathematics) --- Obstruction theory. --- Opérateurs différentiels --- Analyse multidimensionnelle --- Index, Théorie de l' (Mathématiques) --- Théorie des obstructions --- 51 <082.1> --- Mathematics--Series --- Opérateurs différentiels --- Index, Théorie de l' (Mathématiques) --- Théorie des obstructions --- Opérateurs différentiels. --- Index, Théorie de l' (mathématiques) --- Obstructions, Théorie des. --- Differential operators --- Invariants --- Obstruction theory --- Algebraic topology --- Mathematics --- Operators, Differential --- Differential equations --- Operator theory

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Operator theory --- Differential equations --- Boundary value problems --- Differential operators --- Symplectic manifolds --- Manifolds, Symplectic --- Geometry, Differential --- Manifolds (Mathematics) --- Operators, Differential --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Boundary value problems. --- Differential operators. --- Symplectic manifolds. --- Problèmes aux limites. --- Opérateurs différentiels. --- Variétés symplectiques.