发帖
雷达卡
Authors: Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner
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)
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.
Table of contents (14 chapters)
Front Matter
Introduction
Symmetry Breaking Operators and Principal Series Representations of G = O(n+1, 1)
F-method for Matrix-Valued Differential Operators
Matrix-Valued F-method for O(n+1, 1)
Application of Finite-Dimensional Representation Theory
F-system for Symmetry Breaking Operators ( j = i–1, i case)
F-system for Symmetry Breaking Operators ( j = i–2, i+1 case)
Basic Operators in Differential Geometry and Conformal Covariance
Identities of Scalar-Valued Differential Operators DμlDlμ
Construction of Differential Symmetry Breaking Operators
Solutions to Problems A and B for (Sn, Sn–1)
Intertwining Operators
Matrix-Valued Factorization Identities
Appendix: Gegenbauer Polynomials
Back Matter
本帖隐藏的内容
Conformal Symmetry Breaking Operators for Differential Forms on Spheres.pdf
(2.49 MB, 需要: 20 个论坛币)
如果你喜欢我分享的书籍，请关注我：https://bbs.pinggu.org/z_guanzhu.php?action=add&fuid=5975757
订阅我的文库：【金融 + 经济 + 商学 + 国际政治】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3257
【数学 + 统计 + 计算机编程】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3258
【历史 + 心理学 + 社会自然科学】
https://bbs.pinggu.org/forum.php?mod=collection&action=view&ctid=3259
京公网安备 11010802022788号
