Matrix Representations of Groups
Author | : Morris Newman |
Publisher | : |
Total Pages | : 92 |
Release | : 1968 |
Genre | : Matrices |
ISBN | : |
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Author | : Morris Newman |
Publisher | : |
Total Pages | : 92 |
Release | : 1968 |
Genre | : Matrices |
ISBN | : |
Author | : Dudley Ernest Littlewood |
Publisher | : American Mathematical Soc. |
Total Pages | : 322 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821840673 |
Originally written in 1940, this book remains a classical source on representations and characters of finite and compact groups. The book starts with necessary information about matrices, algebras, and groups. Then the author proceeds to representations of finite groups. Of particular interest in this part of the book are several chapters devoted to representations and characters of symmetric groups and the closely related theory of symmetric polynomials. The concluding chapters present the representation theory of classical compact Lie groups, including a detailed description of representations of the unitary and orthogonal groups. The book, which can be read with minimal prerequisites (an undergraduate algebra course), allows the reader to get a good understanding of beautiful classical results about group representations.
Author | : Morris Newman |
Publisher | : Courier Dover Publications |
Total Pages | : 115 |
Release | : 2019-07-17 |
Genre | : Mathematics |
ISBN | : 0486832457 |
Recognizing that the theory of group representations is fundamental to several areas of science and mathematics — including particle physics, crystallography, and group theory — the National Bureau of Standards published this basic but complete exposition of the subject in 1968 in their Applied Mathematics Series. The most significant facts about group representation are developed in an accessible manner, requiring only a familiarity with classical matrix theory. The treatment is rendered self-contained with a series of concise Appendixes that explore elements of the theory of algebraic numbers. Subjects include representations of arbitrary groups, representations of finite groups, multiplication of representations, and bounded representations and Weyl's theorem. All of the important elementary results are featured, a number of advanced topics are discussed, and several special representations are worked out in detail. 1968 edition.
Author | : Dudley E. Littlewood |
Publisher | : |
Total Pages | : 310 |
Release | : 2006 |
Genre | : |
ISBN | : |
Author | : E.B. Vinberg |
Publisher | : Birkhäuser |
Total Pages | : 151 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034892748 |
This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.
Author | : Francis D. Murnaghan |
Publisher | : |
Total Pages | : 392 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : |
Francis D. Murnaghan, a distinguished contributor in the sphere of applied mathematics, created this comprehensive introduction to the theory of group representations. Murnaghan's first-rate account of the field pioneered and developed chiefly by Frobenius, Weyl, and Schur devotes particular attention to the groups—mainly the symmetric group and the rotation group—of fundamental significance for quantum mechanics (especially nuclear physics). Because groups of matrices are the usual group representations, this work is also a valuable contribution to the literature on matrices. The author places particular emphasis on such topics as the theory of group integration, the theory of two-valued or spin representations, the representations of the symmetric group and the analysis of their direct products, the crystallographic groups, and the Lorentz group and the concept of semivectors. Other sections cover groups and matrices, reducibility, group characters, the alternating group, linear groups, and the orthogonal group. This authoritative exposition is of specific interest to teachers and graduate-level students of applied mathematics, physics, and higher algebra.
Author | : Peter Webb |
Publisher | : Cambridge University Press |
Total Pages | : 339 |
Release | : 2016-08-19 |
Genre | : Mathematics |
ISBN | : 1107162394 |
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Author | : J. S. Lomont |
Publisher | : Academic Press |
Total Pages | : 359 |
Release | : 2014-05-12 |
Genre | : Mathematics |
ISBN | : 1483268969 |
Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.
Author | : Benjamin Steinberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 166 |
Release | : 2011-10-23 |
Genre | : Mathematics |
ISBN | : 1461407761 |
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Author | : Pavel I. Etingof |
Publisher | : American Mathematical Soc. |
Total Pages | : 240 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821853511 |
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.