Download or read book Unitary Representations of Groups Duals and Characters written by Bachir Bekka and published by American Mathematical Soc.. This book was released on 2020-11-16 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unitary representations of groups play an important role in many subjects, including number theory, geometry, probability theory, partial differential equations, and quantum mechanics. This monograph focuses on dual spaces associated to a group, which are spaces of building blocks of general unitary representations. Special attention is paid to discrete groups for which the unitary dual, the most common dual space, has proven to be not useful in general and for which other duals spaces have to be considered, such as the primitive dual, the normal quasi-dual, or spaces of characters. The book offers a detailed exposition of these alternative dual spaces and covers the basic facts about unitary representations and operator algebras needed for their study. Complete and elementary proofs are provided for most of the fundamental results that up to now have been accessible only in original papers and appear here for the first time in textbook form. A special feature of this monograph is that the theory is systematically illustrated by a family of examples of discrete groups for which the various dual spaces are discussed in great detail: infinite dihedral group, Heisenberg groups, affine groups of fields, solvable Baumslag-Solitar group, lamplighter group, and general and special linear groups. The book will appeal to graduate students who wish to learn the basics facts of an important topic and provides a useful resource for researchers from a variety of areas. The only prerequisites are a basic background in group theory, measure theory, and operator algebras.
Download or read book Automorphic Representations of Unitary Groups in Three Variables written by Jonathan David Rogawski and published by Princeton University Press. This book was released on 1990-09-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.
Download or read book Poles and Residues of Eisenstein Series for Symplectic and Unitary Groups written by Paul Feit and published by American Mathematical Soc.. This book was released on 1986 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study non-holomorphic Eisenstein series which are defined with respect to the symplectic group over a totally real field, or to the special unitary group of signature ([italic]m, [italic]m) over a CM-field.
Download or read book Automorphic Representation of Unitary Groups in Three Variables AM 123 Volume 123 written by Jonathan David Rogawski and published by Princeton University Press. This book was released on 2016-03-02 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.
Download or read book Endoscopic Classification of Representations of Quasi Split Unitary Groups written by Chung Pang Mok and published by American Mathematical Soc.. This book was released on 2015-04-09 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the author establishes the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.
Download or read book The Unitary Group for the Evaluation of Electronic Energy Matrix Elements written by Jürgen Hinze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last thirty years, with the development of high speed electronic computers, methods have evolved, which permit an accurate and quantitative, ab initio determina tion of the electronic wavefunctions of atoms and molecules. Thus a detailed elucida tion of the electronic energy and structure of molecules has become possible using quantum mechanics directly. Ho\~ever, it is necessary, if such calculations are to yield accurate and reliable results, to include electron correlation explicitely, which requires in general . configuration mixing procedures with an extremely large 5 number of configurations, of the order of 10 configurations. With eigenvalue problems of this size, the limits of even the largest and fastest computers are reached rapidly, and their solution has become possible only, because direct methods have been deve~ loped which permit the determination of eigenvalues and eigenvectors for such large matrices iteratively without constructing the energy matrix explicitely. These direct methods had been limited to the description of closed shell systems, i. e. systems with a single dominant closed shell reference determinant. This limitation arose, because with an open shell reference or with several reference determinants, no procedures were known, which allowed a rapid calculation of the energy matrix elements between configurations with general and widely different spin couplings, which would be necessary. Recently such methods have been developed, based on early work of Gelfand, Biedenharn and Moshinski using a unitary group representation of different spin coupled states; Paldus achieved an extremely compact description.
Download or read book Invariant Measures for Unitary Groups Associated to Kac Moody Lie Algebras written by Doug Pickrell and published by American Mathematical Soc.. This book was released on 2000 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other "invariant measures" are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.
Download or read book Unitary Reflection Groups written by Gustav I. Lehrer and published by Cambridge University Press. This book was released on 2009-08-13 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unitary reflection is a linear transformation of a complex vector space that fixes each point in a hyperplane. Intuitively, it resembles the transformation an image undergoes when it is viewed through a kaleidoscope, or an arrangement of mirrors. This book gives a complete classification of all finite groups which are generated by unitary reflections, using the method of line systems. Irreducible groups are studied in detail, and are identified with finite linear groups. The new invariant theoretic proof of Steinberg's fixed point theorem is treated fully. The same approach is used to develop the theory of eigenspaces of elements of reflection groups and their twisted analogues. This includes an extension of Springer's theory of regular elements to reflection cosets. An appendix outlines links to representation theory, topology and mathematical physics. Containing over 100 exercises, ranging in difficulty from elementary to research level, this book is ideal for honours and graduate students, or for researchers in algebra, topology and mathematical physics. Book jacket.
Download or read book Unitary Symmetry and Elementary Particles written by D Lichtenberg and published by Elsevier. This book was released on 2012-12-02 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unitary Symmetry and Elementary Particles, Second Edition presents the role of symmetry in the study of the physics of the elementary particles. This book discusses the nature and scope of unitary symmetry in physics. Comprised of 12 chapters, this edition starts with an overview of the theories of electromagnetism and gravitation to describe the behavior of certain physical systems. This text then examines the two main categories of the mathematical properties of groups, namely, the properties of abstract groups and the properties of representations of groups. Other chapters consider the use of group theory, which is a significant tool in studying symmetry. This book discusses as well the states that are the basis vectors of irreducible unitary representations of Lie group. The final chapter deals with the quark model, which provides a useful way to understand many properties of hadrons in terms of simpler entities. This book is a valuable resource for physicists.
Download or read book Unitary Symmetry and Combinatorics written by James D. Louck and published by World Scientific. This book was released on 2008 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Notation -- Quantum angular momentum -- Composite systems -- Graphs and adjacency diagrams -- Generating functions -- The D[lambda] polynomials: form -- Operator actions in Hilbert space -- The D[lambda] polynomials: structure -- The general linear and unitary groups -- Tensor operator theory -- Compendium A. Basic algebraic objects -- Compendium B. Combinatorial objects.
Download or read book Algebraic Topology New Trends in Localization and Periodicity written by Carles Broto and published by Birkhäuser. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central to this collection of papers are new developments in the general theory of localization of spaces. This field has undergone tremendous change of late and is yielding new insight into the mysteries of classical homotopy theory. The present volume comprises the refereed articles submitted at the Conference on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. Several comprehensive articles on general localization clarify the basic tools and give a report on the state of the art in the subject matter. The text is therefore accessible not only to the professional mathematician but also to the advanced student.
Download or read book Ergodic Theory and Semisimple Groups written by R.J. Zimmer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course given at the University of Chicago in 1980-81. As with the course, the main motivation of this work is to present an accessible treatment, assuming minimal background, of the profound work of G. A. Margulis concerning rigidity, arithmeticity, and structure of lattices in semi simple groups, and related work of the author on the actions of semisimple groups and their lattice subgroups. In doing so, we develop the necessary prerequisites from earlier work of Borel, Furstenberg, Kazhdan, Moore, and others. One of the difficulties involved in an exposition of this material is the continuous interplay between ideas from the theory of algebraic groups on the one hand and ergodic theory on the other. This, of course, is not so much a mathematical difficulty as a cultural one, as the number of persons comfortable in both areas has not traditionally been large. We hope this work will also serve as a contribution towards improving that situation. While there are a number of satisfactory introductory expositions of the ergodic theory of integer or real line actions, there is no such exposition of the type of ergodic theoretic results with which we shall be dealing (concerning actions of more general groups), and hence we have assumed absolutely no knowledge of ergodic theory (not even the definition of "ergodic") on the part of the reader. All results are developed in full detail.
Download or read book Unitary Representations of Reductive Lie Groups AM 118 Volume 118 written by David A. Vogan Jr. and published by Princeton University Press. This book was released on 2016-03-02 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.
Download or read book Journal of the Chemical Society written by Chemical Society (Great Britain) and published by . This book was released on 1925 with total page 1660 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Titles of chemical papers in British and foreign journals" included in Quarterly journal, v. 1-12.
Download or read book Quarterly Journal of the Chemical Society of London written by Chemical Society (Great Britain) and published by . This book was released on 1925 with total page 1620 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Overgroups of Root Groups in Classical Groups written by Michael Aschbacher and published by American Mathematical Soc.. This book was released on 2016-04-26 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups.
Download or read book The Classification of Finite Simple Groups written by Michael Aschbacher and published by American Mathematical Soc.. This book was released on 2011 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.
