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Conformal symmetry breaking operator...

Kubo, Toshihisa.

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Conformal symmetry breaking operators for differential forms on spheres /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Conformal symmetry breaking operators for differential forms on spheres // Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner.
Author:	Kobayashi, Toshiyuki,
other author:	Kubo, Toshihisa.
Published:	Singapore :Springer, : 2016.,
Description:	ix, 192 p. :ill. ;24 cm.
Subject:	Conformal geometry. -
ISBN:	9789811026560
ISSN:	0075-8434

Conformal symmetry breaking operators for differential forms on spheres /
Kobayashi, Toshiyuki,1962-

Conformal symmetry breaking operators for differential forms on spheres /Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner. - Singapore :Springer,2016. - ix, 192 p. :ill. ;24 cm. - Lecture notes in mathematics,21700075-8434 ;. - Lecture notes in mathematics (Springer-Verlag) ;2170..

Includes bibliographical references (p. 185-186) and index.

This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin-Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valuedfactorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is ageneral method to construct intertwining operators between C8-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate studentsand young researchers in differential geometry, representation theory, and theoretical physics.

ISBN: 9789811026560EUR34.99

ISSN: 0075-8434

LCCN: 2016955062Subjects--Topical Terms:

708569
Conformal geometry.

LC Class. No.: QA329.4

Dewey Class. No.: 515.7242

Conformal symmetry breaking operators for differential forms on spheres /
LDR:02496nam a2200265 a 4500 001 2039474
003 OCoLC
005 20170412021212.0
008 170104s2016 si b b 001 0 eng d
010 $a 2016955062
020 $a 9789811026560 $q (pbk.) : $c EUR34.99
020 $a 9811026564 $q (pbk.)
020 $a 9789811026577 $q (ebk.)
020 $a 9811026572 $q (ebk.)
022 # $a 0075-8434
022 # $a 1617-9692(ebk.)
040 $a VDB $b eng
050 # 4 $a QA329.4
082 0 4 $a 515.7242 $2 23
090 $a QA3 $b .L28 v.2170
100 1 $a Kobayashi, Toshiyuki, $d 1962- $3 1042794
245 1 0 $a Conformal symmetry breaking operators for differential forms on spheres / $c Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner.
260 # $a Singapore : $b Springer, $c 2016.
300 $a ix, 192 p. : $b ill. ; $c 24 cm.
490 1 0 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2170
504 $a Includes bibliographical references (p. 185-186) and index.
520 # $a This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin-Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valuedfactorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is ageneral method to construct intertwining operators between C8-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate studentsand young researchers in differential geometry, representation theory, and theoretical physics.
650 # 0 $a Conformal geometry. $3 708569
650 # 0 $a Differential operators. $3 555718
650 # 0 $a Geometry, Differential. $3 523835
650 # 0 $a Symmetry (Mathematics) $3 629811
700 1 # $a Kubo, Toshihisa. $3 3166094
700 1 # $a Pevzner, Michael, $d 1971- $3 3166095
830 0 $a Lecture notes in mathematics (Springer-Verlag) ; $v 2170. $3 3166096