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Introduction To Orthogonal Symplectic And Unitary Representations Of Finite Groups
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Book Synopsis Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups by : Carl R. Riehm
Download or read book Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups written by Carl R. Riehm and published by American Mathematical Soc.. This book was released on 2011 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics--linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms--and thus inherit some of the characteristics of both. This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the ``classical'' fields--algebraically closed, real closed, finite, local and global. A detailed exposition of the background material needed is given in the first chapter. It was A. Frohlich who first gave a systematic organization of this subject, in a series of papers beginning in 1969. His paper Orthogonal and symplectic representations of groups represents the culmination of his published work on orthogonal and symplectic representations. The author has included most of the work from that paper, extending it to include unitary representations, and also providing new approaches, such as the use of the equivariant Brauer-Wall group in describing the principal invariants of orthogonal representations and their interplay with each other.
Book Synopsis Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups by : Carl R. Riehm
Download or read book Introduction to Orthogonal, Symplectic, and Unitary Representations of Finite Groups written by Carl R. Riehm and published by American Mathematical Soc.. This book was released on with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representations of Finite Groups of Lie Type by : François Digne
Download or read book Representations of Finite Groups of Lie Type written by François Digne and published by Cambridge University Press. This book was released on 1991-04-26 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne-Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.
Book Synopsis The Classical Groups by : Hermann Weyl
Download or read book The Classical Groups written by Hermann Weyl and published by Princeton University Press. This book was released on 1946 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author discusses symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are important in understanding the group-theoretic structure of quantum mechanics.
Author :Calif.) Arcata Conference on Representations of Finite Groups (1986 : Arcata Publisher :American Mathematical Soc. ISBN 13 :0821814788 Total Pages :552 pages Book Rating :4.8/5 (218 download)
Book Synopsis The Arcata Conference on Representations of Finite Groups, Part 2 by : Calif.) Arcata Conference on Representations of Finite Groups (1986 : Arcata
Download or read book The Arcata Conference on Representations of Finite Groups, Part 2 written by Calif.) Arcata Conference on Representations of Finite Groups (1986 : Arcata and published by American Mathematical Soc.. This book was released on 1987 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representation Theory of Finite Groups and Finite-Dimensional Algebras by : Michler
Download or read book Representation Theory of Finite Groups and Finite-Dimensional Algebras written by Michler and published by Birkhäuser. This book was released on 2012-12-06 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.
Book Synopsis The Endoscopic Classification of Representations Orthogonal and Symplectic Groups by : James Arthur
Download or read book The Endoscopic Classification of Representations Orthogonal and Symplectic Groups written by James Arthur and published by American Mathematical Soc.. This book was released on 2013-10-31 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the Langlands program, endoscopy is a fundamental process for relating automorphic representations of one group with those of another. In this book, Arthur establishes an endoscopic classification of automorphic representations of orthogonal and symplectic groups . The representations are shown to occur in families (known as global -packets and -packets), which are parametrized by certain self-dual automorphic representations of an associated general linear group . The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of for any representation in a family. The results of the volume have already had significant applications: to the local Langlands correspondence, the construction of unitary representations, the existence of Whittaker models, the analytic behaviour of Langlands -functions, the spectral theory of certain locally symmetric spaces, and to new phenomena for symplectic epsilon-factors. One can expect many more. In fact, it is likely that both the results and the techniques of the volume will have applications to almost all sides of the Langlands program. The methods are by comparison of the trace formula of with its stabilization (and a comparison of the twisted trace formula of with its stabilization, which is part of work in progress by Moeglin and Waldspurger). This approach is quite different from methods that are based on -functions, converse theorems, or the theta correspondence. The comparison of trace formulas in the volume ought to be applicable to a much larger class of groups. Any extension at all will have further important implications for the Langlands program.
Book Synopsis Introduction to Mathematical Physics by : Michael T. Vaughn
Download or read book Introduction to Mathematical Physics written by Michael T. Vaughn and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive survey of all the mathematical methods that should be available to graduate students in physics. In addition to the usual topics of analysis, such as infinite series, functions of a complex variable and some differential equations as well as linear vector spaces, this book includes a more extensive discussion of group theory than can be found in other current textbooks. The main feature of this textbook is its extensive treatment of geometrical methods as applied to physics. With its introduction of differentiable manifolds and a discussion of vectors and forms on such manifolds as part of a first-year graduate course in mathematical methods, the text allows students to grasp at an early stage the contemporary literature on dynamical systems, solitons and related topological solutions to field equations, gauge theories, gravitational theory, and even string theory. Free solutions manual available for lecturers at www.wiley-vch.de/supplements/.
Book Synopsis An Introduction to the Representation Theory of Groups by : Emmanuel Kowalski
Download or read book An Introduction to the Representation Theory of Groups written by Emmanuel Kowalski and published by American Mathematical Society. This book was released on 2014-08-28 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.
Book Synopsis Unitary Representations of Maximal Parabolic Subgroups of the Classical Groups by : Joseph Albert Wolf
Download or read book Unitary Representations of Maximal Parabolic Subgroups of the Classical Groups written by Joseph Albert Wolf and published by American Mathematical Soc.. This book was released on 1976 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representations of Finite Groups of Lie Type by : François Digne
Download or read book Representations of Finite Groups of Lie Type written by François Digne and published by Cambridge University Press. This book was released on 2020-03-05 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.
Book Synopsis Explicit Brauer Induction by : Victor Percy Snaith
Download or read book Explicit Brauer Induction written by Victor Percy Snaith and published by Cambridge University Press. This book was released on 1994-10-27 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1994 book gave, for the first time, an entirely algebraic treatment of the technique of Explicit Brauer Induction.
Book Synopsis An Introduction to Harmonic Analysis on Semisimple Lie Groups by : V. S. Varadarajan
Download or read book An Introduction to Harmonic Analysis on Semisimple Lie Groups written by V. S. Varadarajan and published by Cambridge University Press. This book was released on 1999-07-22 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.
Book Synopsis An Introduction to the Representation Theory of Groups by : Emmanuel Kowalski
Download or read book An Introduction to the Representation Theory of Groups written by Emmanuel Kowalski and published by . This book was released on 2014 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Xivth International Congress On Mathematical Physics by : Jean-claude Zambrini
Download or read book Xivth International Congress On Mathematical Physics written by Jean-claude Zambrini and published by World Scientific. This book was released on 2006-03-07 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen «On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory»; A Chenciner «Symmetries and “simple” solutions of the classical n-body problem»; M J Esteban «Relativistic models in atomic and molecular physics»; K Fredenhagen «Locally covariant quantum field theory»; K Gawedzki «Simple models of turbulent transport»; I Krichever «Algebraic versus Liouville integrability of the soliton systems»; R V Moody «Long-range order and diffraction in mathematical quasicrystals»; S Smirnov «Critical percolation and conformal invariance»; J P Solovej «The energy of charged matter»; V Schomerus «Strings through the microscope»; C Villani «Entropy production and convergence to equilibrium for the Boltzmann equation»; D Voiculescu «Aspects of free probability».The book collects as well carefully selected invited Session Talks in: Dynamical Systems, Integrable Systems and Random Matrix Theory, Condensed Matter Physics, Equilibrium Statistical Mechanics, Quantum Field Theory, Operator Algebras and Quantum Information, String and M Theory, Fluid Dynamics and Nonlinear PDE, General Relativity, Nonequilibrium Statistical Mechanics, Quantum Mechanics and Spectral Theory, Path Integrals and Stochastic Analysis.
Book Synopsis Robert Steinberg Collected Papers by : Robert Steinberg
Download or read book Robert Steinberg Collected Papers written by Robert Steinberg and published by American Mathematical Soc.. This book was released on 1997 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of published papers by Robert Steinberg. It contains all of his published papers on group theory, including those on "special" representations (now called Steinberg representations), Coxeter groups, regular nilpotent elements and Galois cohomology. After each paper, there is a section, "Comments on the papers", that contains minor corrections and clarifications and explains how ideas and results have evolved and been used since they first appeared.
Book Synopsis The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic by : Irina D. Suprunenko
Download or read book The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic written by Irina D. Suprunenko and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The minimal polynomials of the images of unipotent elements in irreducible rational representations of the classical algebraic groups over fields of odd characteristic are found. These polynomials have the form $(t-1)^d$ and hence are completely determined by their degrees. In positive characteristic the degree of such polynomial cannot exceed the order of a relevant element. It occurs that for each unipotent element the degree of its minimal polynomial in an irreducible representation is equal to the order of this element provided the highest weight of the representation is large enough with respect to the ground field characteristic. On the other hand, classes of unipotent elements for which in every nontrivial representation the degree of the minimal polynomial is equal to the order of the element are indicated. In the general case the problem of computing the minimal polynomial of the image of a given element of order $p^s$ in a fixed irreducible representation of a classical group over a field of characteristic $p>2$ can be reduced to a similar problem for certain $s$ unipotent elements and a certain irreducible representation of some semisimple group over the field of complex numbers. For the latter problem an explicit algorithm is given. Results of explicit computations for groups of small ranks are contained in Tables I-XII. The article may be regarded as a contribution to the programme of extending the fundamental results of Hall and Higman (1956) on the minimal polynomials from $p$-solvable linear groups to semisimple groups.
