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作者 Kobayashi, Toshiyuki, 1962- author
書名 Symmetry breaking for representations of rank one orthogonal groups II / Toshiyuki Kobayashi, Birgit Speh
出版項 Singapore : Springer, [2018]
2018
國際標準書號 9811329001
9789811329005
國際標準號碼 10.1007/978-981-13-2901-2
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA174.7.S96 K63 2018    在架上    30340200561185
說明 xv, 342 pages : illustrations ; 24 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
系列 Lecture notes in mathematics, 0075-8434 ; 2234
Lecture notes in mathematics (Springer-Verlag) ; 2234. 0075-8434
附註 Includes bibliographical references (pages 333-336) and index
"This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup. The study of symmetry breaking operators (intertwining operators for restriction) is an important and very active research area in modern representation theory, which also interacts with various fields in mathematics and theoretical physics ranging from number theory to differential geometry and quantum mechanics. The first author initiated a program of the general study of symmetry breaking operators. The present book pursues the program by introducing new ideas and techniques, giving a systematic and detailed treatment in the case of orthogonal groups of real rank one, which will serve as models for further research in other settings. In connection to automorphic forms, this work includes a proof for a multiplicity conjecture by Gross and Prasad for tempered principal series representations in the case (SO(n + 1, 1), SO(n, 1)). The authors propose a further multiplicity conjecture for nontempered representations. Viewed from differential geometry, this seminal work accomplishes the classification of all conformally covariant operators transforming differential forms on a Riemanniann manifold X to those on a submanifold in the model space (X, Y) = (Sn, Sn-1). Functional equations and explicit formulae of these operators are also established. This book offers a self-contained and inspiring 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 representation theory, automorphic forms, differential geometry, and theoretical physics"--Page 4 of cover
主題 Symmetry (Mathematics)
Broken symmetry (Physics) -- Mathematics
Lie groups -- Analysis
Conformal geometry
Alt Author Speh, Birgit, 1949- author
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