Unitary Representations Of Maximal Parabolic Subgroups Of The Classical Groups
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Unitary Representations Of Maximal Parabolic Subgroups Of The Classical Groups
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Author : Joseph Albert Wolf
language : en
Publisher: American Mathematical Soc.
Release Date : 1976
Unitary Representations Of Maximal Parabolic Subgroups Of The Classical Groups written by Joseph Albert Wolf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
All the irreducible unitary representations are found, in an explicit way, for the maximal parabolic subgroups in the various classical series of real and complex Lie groups. In each case, the nilradical is similar to the Heisenberg group, and its representations come out of the Kirillov orbit method. Then the representations of the parabolic subgroup are worked out from Mackey's little group method. The little group usually belongs to a different classical series--but with smaller matrices--so the end result in each series is a recursive statement involving several series.
Unitary Representations Of Maximal Parabolic Subgroups Of The Classical Groups
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Author : Joseph A. Wolf
language : en
Publisher:
Release Date :
Unitary Representations Of Maximal Parabolic Subgroups Of The Classical Groups written by Joseph A. Wolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Unitary Representations Of Maximal Parabolic Subgroups Of The Classical Groups
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Author : A. K. Bousfield
language : en
Publisher:
Release Date : 1976
Unitary Representations Of Maximal Parabolic Subgroups Of The Classical Groups written by A. K. Bousfield and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Algebra, Homological categories.
Classification And Fourier Inversion For Parabolic Subgroups With Square Integrable Nilradical
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Author : Joseph Albert Wolf
language : en
Publisher: American Mathematical Soc.
Release Date : 1979
Classification And Fourier Inversion For Parabolic Subgroups With Square Integrable Nilradical written by Joseph Albert Wolf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
In recent years a general theory has been developed for inverting Fourier transforms on non-unimodular locally compact groups. The few known explicit examples have been solvable or have fit into the framework: parabolic subgroup of semisimple Lie group, in which the nilradical has square integrable representations. That class of parabolic subgroups is interesting in its own right; it occurs in many geometric situations, and it has a large overlap with the class of maximal parabolic subgroups.
Unitary Representations And Harmonic Analysis
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Author : M. Sugiura
language : en
Publisher: Elsevier
Release Date : 1990-03-01
Unitary Representations And Harmonic Analysis written by M. Sugiura and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-01 with Mathematics categories.
The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.
Noncompact Semisimple Lie Algebras And Groups
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Author : Vladimir K. Dobrev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-09-12
Noncompact Semisimple Lie Algebras And Groups written by Vladimir K. Dobrev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-12 with Mathematics categories.
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory supplemented by many concrete examples for a great variety of noncompact semisimple Lie algebras and groups. Contents: Introduction Lie Algebras and Groups Real Semisimple Lie Algebras Invariant Differential Operators Case of the Anti-de Sitter Group Conformal Case in 4D Kazhdan–Lusztig Polynomials, Subsingular Vectors, and Conditionally Invariant Equations Invariant Differential Operators for Noncompact Lie Algebras Parabolically Related to Conformal Lie Algebras Multilinear Invariant Differential Operators from New Generalized Verma Modules Bibliography Author Index Subject Index
Noncompact Lie Groups And Some Of Their Applications
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Author : Elizabeth A. Tanner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Noncompact Lie Groups And Some Of Their Applications written by Elizabeth A. Tanner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr.
Theory Of Group Representations And Applications
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Author : Ryszard Raczka
language : en
Publisher: World Scientific Publishing Company
Release Date : 1986-11-01
Theory Of Group Representations And Applications written by Ryszard Raczka and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-11-01 with Science categories.
The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations.
Generic Representations Of Parabolic Subgroups Of The Classical Groups
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Author : Alexander Dvorsky
language : en
Publisher:
Release Date : 1996
Generic Representations Of Parabolic Subgroups Of The Classical Groups written by Alexander Dvorsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Variations On A Theme By Kepler
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Author : Victor Guillemin
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Variations On A Theme By Kepler written by Victor Guillemin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This book is based on the Colloquium Lectures presented by Shlomo Sternberg in 1990. The authors delve into the mysterious role that groups, especially Lie groups, play in revealing the laws of nature by focusing on the familiar example of Kepler motion: the motion of a planet under the attraction of the sun according to Kepler's laws. Newton realized that Kepler's second law--that equal areas are swept out in equal times--has to do with the fact that the force is directed radially to the sun. Kepler's second law is really the assertion of the conservation of angular momentum, reflecting the rotational symmetry of the system about the origin of the force. In today's language, we would say that the group $O(3)$ (the orthogonal group in three dimensions) is responsible for Kepler's second law. By the end of the nineteenth century, the inverse square law of attraction was seen to have $O(4)$ symmetry (where $O(4)$ acts on a portion of the six-dimensional phase space of the planet). Even larger groups have since been found to be involved in Kepler motion. In quantum mechanics, the example of Kepler motion manifests itself as the hydrogen atom. Exploring this circle of ideas, the first part of the book was written with the general mathematical reader in mind. The remainder of the book is aimed at specialists. It begins with a demonstration that the Kepler problem and the hydrogen atom exhibit $O(4)$ symmetry and that the form of this symmetry determines the inverse square law in classical mechanics and the spectrum of the hydrogen atom in quantum mechanics. The space of regularized elliptical motions of the Kepler problem (also known as the Kepler manifold) plays a central role in this book. The last portion of the book studies the various cosmological models in this same conformal class (and having varying isometry groups) from the viewpoint of projective geometry. The computation of the hydrogen spectrum provides an illustration of the principle that enlarging the phase space can simplify the equations of motion in the classical setting and aid in the quantization problem in the quantum setting. The authors provide a short summary of the homological quantization of constraints and a list of recent applications to many interesting finite-dimensional settings. The book closes with an outline of Kostant's theory, in which a unitary representation is associated to the minimal nilpotent orbit of $SO(4,4)$ and in which electromagnetism and gravitation are unified in a Kaluza-Klein-type theory in six dimensions.