LEADER 00874nam a22002291i 4500 001 991004148319707536 005 20021112151255.0 008 020814s1962 be |||||||||||||||||fre 035 $ab11923027-39ule_inst 035 $aocm00000004$9ExL 040 $aDip.to Filologia Ling. e Lett.$bita$cA.t.i. Arché s.c.r.l. Pandora Sicilia s.r.l. 100 1 $aBal, Willy$0191919 245 10$aIntroduction à la linguistique /$cWilly Bal 260 $aLéopoldville :$bUniversité Lovaniuin,$c1962 300 $a273 p. ;$c24 cm 650 4$aLinguistica 907 $a.b11923027$b02-04-14$c01-04-03 912 $a991004148319707536 945 $aLE008 FL.M. (f.r.) VII 8$g1$i2008000496821$lle008$o-$pE0.00$q-$rl$s- $t0$u0$v0$w0$x0$y.i12194086$z01-04-03 996 $aIntroduction à la linguistique$9914827 997 $aUNISALENTO 998 $ale008$b01-04-03$cm$da $e-$ffre$gbe $h0$i1 LEADER 06294nam 22006853 450 001 9910959539903321 005 20220905084604.0 010 $a9781470463397 010 $a1470463393 035 $a(CKB)5490000000082080 035 $a(MiAaPQ)EBC29731906 035 $a(Au-PeEL)EBL29731906 035 $a(OCoLC)1289816395 035 $a(RPAM)21986788 035 $a(PPN)256595372 035 $a(EXLCZ)995490000000082080 100 $a20220905d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConformal Symmetry Breaking Differential Operators on Differential Forms 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$d©2020. 215 $a1 online resource (124 pages) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 1304 311 08$a9781470443245 311 08$a1470443244 320 $aIncludes bibliographical references. 327 $aCover -- 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. 330 $a"We study conformal symmetry breaking differential operators which map differential forms on Rn to differential forms on a codimension one subspace Rn-1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn-1. They correspond to homomorphisms of generalized Verma modules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F-method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the related branching problems restricting generalized Verma modules for so(n+1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking differential operators in terms of the first-order operators d, ?, d and ? and certain hypergeometric polynomials. A dominant role in these studies is played by two infinite sequences of symmetry breaking differential operators which depend on a complex parameter ?. Their values at special values of ? appear as factors in two systems of factorization identities which involve the Branson-Gover operators of the Euclidean metrics on Rn and Rn-1 and the operators d, ?, d and ? as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn-1, respectively"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vno. 1304. 606 $aDifferential operators 606 $aConformal geometry 606 $aSymmetry (Mathematics) 606 $aTopological 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, see$2msc 606 $aPartial differential equations -- Elliptic equations and systems [See also 58J10, 58J20] -- Higher-order elliptic equations [See also 31A30, 31B30]$2msc 606 $aDifferential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Classical differential geometry -- Conformal differential geometry$2msc 606 $aSpecial 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; for$2msc 615 0$aDifferential operators. 615 0$aConformal geometry. 615 0$aSymmetry (Mathematics) 615 7$aTopological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX} -- Lie groups {For the topology of Lie groups and homogeneous spaces, see 615 7$aPartial differential equations -- Elliptic equations and systems [See also 58J10, 58J20] -- Higher-order elliptic equations [See also 31A30, 31B30]. 615 7$aDifferential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Classical differential geometry -- Conformal differential geometry. 615 7$aSpecial 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; for 676 $a516.3/5 686 $a22E46$a35J30$a53A30$a22E47$a33C45$2msc 700 $aFischmann$b Matthias$01801187 701 $aJuhl$b Andreas$066004 701 $aSomberg$b Petr$01801188 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910959539903321 996 $aConformal Symmetry Breaking Differential Operators on Differential Forms$94346309 997 $aUNINA