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005			20240729131156.0
006			m o d |
007			cr cnu||||||||
008			240724s2015 xx o ||||0 eng d
020			_a9781470426156 _q(electronic bk.)
020			_z9781470419226
035			_a(MiAaPQ)EBC4832036
035			_a(Au-PeEL)EBL4832036
035			_a(CaPaEBR)ebr11367321
035			_a(OCoLC)920024642
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQC793.3.S9.K633 2015
082	0		_a12/.482
100	1		_aKobayashi, Toshiyuki.
245	1	0	_aSymmetry Breaking for Representations of Rank One Orthogonal Groups.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2015.
264		4	_c©2015.
300			_a1 online resource (124 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.238
505	0		_aCover -- Title page -- Chapter 1. Introduction -- Chapter 2. Symmetry breaking for the spherical principal series representations -- 2.1. Notation and review of previous results -- 2.2. Finite-dimensional subquotients of disconnected groups -- 2.3. Symmetry breaking operators and spherical principal series representations -- 2.4. Multiplicities for composition factors -- Chapter 3. Symmetry breaking operators -- 3.1. Restriction of representations and symmetry breaking operators -- 3.2. Distribution kernels of symmetry breaking operators -- 3.3. Differential intertwining operators -- 3.4. Smooth representations and intertwining operators -- 3.5. Symmetry breaking operators for principal series representations -- 3.6. Meromorphic continuation of symmetry breaking operators -- Chapter 4. More about principal series representations -- 4.1. Models of principal series representations -- 4.2. Explicit -finite functions in the non-compact model -- 4.3. Normalized Knapp-Stein intertwining operator -- Chapter 5. Double coset decomposition '\ / -- Chapter 6. Differential equations satisfied by the distribution kernels of symmetry breaking operators -- 6.1. A system of differential equations for symmetry breaking operators -- 6.2. The solutions ℴ (ℝⁿ∖{0} -- , ) -- Chapter 7. -finite vectors and regular symmetry breaking operators ̃ _{ , } -- 7.1. Distribution kernel \ka{ } and its normalization -- 7.2. Preliminary results -- 7.3. Proof of Proposition 7.3 -- Chapter 8. Meromorphic continuation of regular symmetry breaking operators \ka{ } -- 8.1. Recurrence relations of the distribution kernels \ka{ } -- 8.2. Functional equations -- 8.3. 8.3 Support of \KA{ } -- 8.4. Renormalization \AAt_{ , } for ∈-ℕ -- Chapter 9. Singular symmetry breaking operator \B_{ , } -- 9.1. Singular symmetry breaking operator \B_{ , }.
505	8		_a9.2. -finite vectors and singular operators \tB{ } -- 9.3. Proof of Theorem 9.1 -- 9.4. Support of the distribution kernel of \B_{ , } -- 9.5. Renormalization \BB_{ , } for \nulambda∈ _{ } with odd -- Chapter 10. Differential symmetry breaking operators -- 10.1. Power of the Laplacian -- 10.2. Juhl's family of differential operators -- 10.3. The kernel of the differential symmetry breaking operator \C_{ , } -- Chapter 11. Classification of symmetry breaking operators -- 11.1. Classification of symmetry breaking operators -- 11.2. Strategy of the proof of Theorem 11.1 -- 11.3. Lower bounds of the multiplicities -- 11.4. Extension of solutions from ℝⁿ∖{0} to ℝⁿ -- 11.5. Regular symmetry breaking operators -- 11.6. Singular symmetry breaking operators -- Chapter 12. Residue formulae and functional identities -- 12.1. Residues of symmetry breaking operators -- 12.2. Functional equations satisfied by singular symmetry breaking operators -- Chapter 13. Image of symmetry breaking operators -- 13.1. Finite-dimensional image for ∈-ℕ -- 13.2. Image for ∈ +ℕ -- 13.3. Spherical vectors and symmetry breaking operators -- Chapter 14. Application to analysis on anti-de Sitter space -- 14.1. Harmonic analysis on Lorentzian hyperbolic spaces -- 14.2. Application of symmetry breaking operators to anti-de Sitter spaces -- 14.3. Analysis on vector bundles over anti-de Sitter spaces -- Chapter 15. Application to branching laws of complementary series -- 15.1. Discrete spectrum in complementary series -- 15.2. ²-model of complementary series representations -- Chapter 16. Appendix -- 16.1. Gegenbauer polynomials -- 16.2. -Bessel function and its renormalization -- 16.3. Zuckerman derived functor modules _{ }( ) -- Acknowledgments -- References -- List of Symbols -- Back Cover.
520			_aThe authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of G=O(n+1,1) and G'=O(n,1). They construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explicitly. Symmetry breaking operators at exceptional discrete parameters are thoroughly studied. The authors obtain closed formulae for the functional equations which the composition of the symmetry breaking operators with the Knapp--Stein intertwining operators of G and G' satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of G and G'. Some applications are included.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aBroken symmetry (Physics).
655		4	_aElectronic books.
700	1		_aSpeh, Birgit.
776	0	8	_iPrint version: _aKobayashi, Toshiyuki _tSymmetry Breaking for Representations of Rank One Orthogonal Groups _dProvidence : American Mathematical Society,c2015 _z9781470419226
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4832036 _zClick to View
999			_c124856 _d124856