06294nam 22006853 450 991095953990332120220905084604.097814704633971470463393(CKB)5490000000082080(MiAaPQ)EBC29731906(Au-PeEL)EBL29731906(OCoLC)1289816395(RPAM)21986788(PPN)256595372(EXLCZ)99549000000008208020220905d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierConformal Symmetry Breaking Differential Operators on Differential Forms1st ed.Providence :American Mathematical Society,2021.©2020.1 online resource (124 pages)Memoirs of the American Mathematical Society,0065-9266 ;Number 13049781470443245 1470443244 Includes bibliographical references.Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. The -method -- 2.2. Notation and induced representations -- 2.3. A branching problem -- Chapter 3. Singular vectors -- 3.1. The \gol′-equivariance -- 3.2. Families of singular vectors of the first type -- 3.3. Families of singular vectors of the second type -- 3.4. Singular vectors of the third type -- 3.5. Singular vectors of the fourth type -- 3.6. Middle degree cases -- Chapter 4. Conformal symmetry breaking differential operators on differential forms -- 4.1. Families of the first type -- 4.2. Families of the second type -- 4.3. Hodge conjugation -- 4.4. Operators of the third type -- 4.5. Operators of the fourth type -- 4.6. Operators on middle degree forms -- 4.7. Proof of Theorem 3 -- 4.8. Examples -- Chapter 5. Geometric formulas for conformal symmetry breaking operators -- 5.1. Preparations -- 5.2. Even-order families of the first and second type -- 5.3. Odd-order families of the first and second type -- 5.4. Operators of the third and fourth type -- Chapter 6. Factorization identities for conformal symmetry breaking operators -- 6.1. Branson-Gover, gauge companion and -curvature operators -- 6.2. Main factorizations -- 6.3. Supplementary factorizations -- 6.4. Applications -- Appendix: Gegenbauer and Jacobi polynomials -- Bibliography -- Back Cover."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"--Provided by publisher.Memoirs of the American Mathematical Society ;no. 1304.Differential operatorsConformal geometrySymmetry (Mathematics)Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX} -- Lie groups {For the topology of Lie groups and homogeneous spaces, seemscPartial differential equations -- Elliptic equations and systems [See also 58J10, 58J20] -- Higher-order elliptic equations [See also 31A30, 31B30]mscDifferential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Classical differential geometry -- Conformal differential geometrymscSpecial functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; formscDifferential operators.Conformal geometry.Symmetry (Mathematics)Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX} -- Lie groups {For the topology of Lie groups and homogeneous spaces, seePartial differential equations -- Elliptic equations and systems [See also 58J10, 58J20] -- Higher-order elliptic equations [See also 31A30, 31B30].Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Classical differential geometry -- Conformal differential geometry.Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for516.3/522E4635J3053A3022E4733C45mscFischmann Matthias1801187Juhl Andreas66004Somberg Petr1801188MiAaPQMiAaPQMiAaPQBOOK9910959539903321Conformal Symmetry Breaking Differential Operators on Differential Forms4346309UNINA