Symmetry Breaking for Representations of Rank One Orthogonal Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetry Breaking for Representations of Rank One Orthogonal Groups write by Toshiyuki Kobayashi. This book was released on 2015-10-27. Symmetry Breaking for Representations of Rank One Orthogonal Groups available in PDF, EPUB and Kindle. The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of and . 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 and satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of and . Some applications are included.
Symmetry Breaking for Representations of Rank One Orthogonal Groups II
Symmetry Breaking for Representations of Rank One Orthogonal Groups II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetry Breaking for Representations of Rank One Orthogonal Groups II write by Toshiyuki Kobayashi. This book was released on 2018-12-27. Symmetry Breaking for Representations of Rank One Orthogonal Groups II available in PDF, EPUB and Kindle. 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 formulæ 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.
Symmetry Breaking for Representations of Rank One Orthogonal Groups
Symmetry Breaking for Representations of Rank One Orthogonal Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetry Breaking for Representations of Rank One Orthogonal Groups write by Toshiyuki Kobayashi. This book was released on 2015. Symmetry Breaking for Representations of Rank One Orthogonal Groups available in PDF, EPUB and Kindle.
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 write by Vladimir Dobrev. This book was released on 2018-11-28. Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 available in PDF, EPUB and Kindle. This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.
Lie Theory and Its Applications in Physics
Lie Theory and Its Applications in Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Theory and Its Applications in Physics write by Vladimir Dobrev. This book was released on 2020-10-15. Lie Theory and Its Applications in Physics available in PDF, EPUB and Kindle. This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
