Conformal Symmetry Breaking Operators for Differential Forms on Spheres: Lecture Notes in Mathematics, cartea 2170
Autor Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzneren Limba Engleză Paperback – 12 oct 2016
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-valued factorization 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 a general method to construct intertwining operators between C∞-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 students and young researchers in differential geometry, representation theory, and theoretical physics.
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Specificații
ISBN-13: 9789811026560
ISBN-10: 9811026564
Pagini: 200
Ilustrații: IX, 192 p.
Dimensiuni: 155 x 235 mm
Greutate: 0.4 kg
Ediția:1st ed. 2016
Editura: Springer Nature Singapore
Colecția Springer
Seria Lecture Notes in Mathematics
Locul publicării:Singapore, Singapore
ISBN-10: 9811026564
Pagini: 200
Ilustrații: IX, 192 p.
Dimensiuni: 155 x 235 mm
Greutate: 0.4 kg
Ediția:1st ed. 2016
Editura: Springer Nature Singapore
Colecția Springer
Seria Lecture Notes in Mathematics
Locul publicării:Singapore, Singapore
Cuprins
Textul de pe ultima copertă
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-valued factorization 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 a general method to construct intertwining operators between C∞-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 students and young researchers in differential geometry, representation theory, and theoretical physics.
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-valued factorization 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 a general method to construct intertwining operators between C∞-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 students and young researchers in differential geometry, representation theory, and theoretical physics.
Caracteristici
Introduces a cutting-edge method for effective construction of symmetry breaking operators for branching rules in representation theory Includes hot topics of conformal geometry and global analysis as applications of representation theory Provides the complete classification of all conformally equivariant differential operators on forms on the model space (Sn, Sn-1)