Group Matrices Group Determinants And Representation Theory
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| Author | : Kenneth W. Johnson |
| Publisher | : Springer Nature |
| Total Pages | : 384 |
| Release | : 2019-11-08 |
| Genre | : Mathematics |
| ISBN | : 3030283003 |
This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science. The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.
| 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 | : Gregory Karpilovsky |
| Publisher | : Elsevier |
| Total Pages | : 973 |
| Release | : 2016-06-06 |
| Genre | : Mathematics |
| ISBN | : 1483295109 |
This volume is divided into three parts. Part I provides the foundations of the theory of modular representations. Special attention is drawn to the Brauer-Swan theory and the theory of Brauer characters. A detailed investigation of quadratic, symplectic and symmetric modules is also provided. Part II is devoted entirely to the Green theory: vertices and sources, the Green correspondence, the Green ring, etc. In Part III, permutation modules are investigated with an emphasis on the study of p-permutation modules and Burnside rings. The material is developed with sufficient attention to detail so that it can easily be read by the novice, although its chief appeal will be to specialists. A number of the results presented in this volume have almost certainly never been published before.
| Author | : Victor E Hill |
| Publisher | : CRC Press |
| Total Pages | : 238 |
| Release | : 2018-12-12 |
| Genre | : Mathematics |
| ISBN | : 1351443801 |
Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. This book offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, it emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The text includes sections that provide the mathematical basis for some of the applications of group theory. It also offers numerous exercises, some stressing computation of concrete examples, others stressing development of the theory.
| Author | : Asim Orhan Barut |
| Publisher | : World Scientific |
| Total Pages | : 750 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : 9789971502171 |
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
| Author | : Martin Burrow |
| Publisher | : Courier Corporation |
| Total Pages | : 210 |
| Release | : 2014-05-05 |
| Genre | : Mathematics |
| ISBN | : 0486145077 |
DIVConcise, graduate-level exposition covers representation theory of rings with identity, representation theory of finite groups, more. Exercises. Appendix. 1965 edition. /div
| Author | : Gilbert de Beauregard Robinson |
| Publisher | : Edinburgh : University Press |
| Total Pages | : 218 |
| Release | : 1961 |
| Genre | : Group theory |
| ISBN | : |
| Author | : Meinolf Geck |
| Publisher | : EPFL Press |
| Total Pages | : 472 |
| Release | : 2007-05-07 |
| Genre | : Mathematics |
| ISBN | : 9780849392436 |
After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a very large field of study. This progress, and the remaining open problems (e.g., the conjectures of Alterin, Dade, Broué, James, etc.) have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: Broué (Finite reductive groups and spetses); Carlson (Cohomology and representations of finite groups); Geck (Representations of Hecke algebras); Seitz (Topics in algebraic groups); Kessar and Linckelmann (Fusion systems and blocks); Serre (On finite subgroups of Lie groups); Thévenaz (The classification of endo-permutaion modules); and Webb (Representations and cohomology of categories).
| Author | : Larry L. Dornhoff |
| Publisher | : |
| Total Pages | : 282 |
| Release | : 1971 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Gordon James |
| Publisher | : Cambridge University Press |
| Total Pages | : 436 |
| Release | : 2001-10-18 |
| Genre | : Mathematics |
| ISBN | : 1139811053 |
This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.
