Classical Groups And Related Topics

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Classical Groups And Related Topics

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Author : Alexander Hahn
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Classical Groups And Related Topics written by Alexander Hahn 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 1989 with Mathematics categories.

During his lifetime, L. K. Hua played a leading role in and exerted a great influence upon the development in China of modern mathematics, both pure and applied. His mathematical career began in 1931 at Tsinghua University where he continued as a professor for many years. Hua made many significant contributions to number theory, algebra, geometry, complex analysis, numerical analysis, and operations research. In particular, he initiated the study of classical groups in China and developed new matrix methods which, as applied by him as well as his followers, were instrumental in the successful attack of many problems. To honor his memory, a joint China-U.S. conference on Classical Groups and Related Topics was held at Tsinghua University in Beijing in May 1987. This volume represents the proceedings of that conference and contains both survey articles and research papers focusing on classical groups and closely related topics.

Representations And Invariants Of The Classical Groups

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Author : Roe Goodman
language : en
Publisher: Cambridge University Press
Release Date : 2000-01-13

Representations And Invariants Of The Classical Groups written by Roe Goodman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-13 with Mathematics categories.

More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.

Representation Of Lie Groups And Related Topics

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Author : Anatoliĭ Moiseevich Vershik
language : en
Publisher: CRC Press
Release Date : 1990

Representation Of Lie Groups And Related Topics written by Anatoliĭ Moiseevich Vershik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

Eight papers provide mature readers with careful review of progress (through about 1983) toward the creation of a theory of the representations of infinite-dimensional Lie groups and algebras, and of some related topics. Recent developments in physics have provided major impetus for the development of such a theory, and the volume will be of special interest to mathematical physicists (quantum field theorists). Translated from the Russian edition of unstated date, and beautifully produced (which--at the price--it should be!). Book club price, $118. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

The Topology Of Classical Groups And Related Topics

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Author : S. Y. Husseini
language : en
Publisher: CRC Press
Release Date : 1969

The Topology Of Classical Groups And Related Topics written by S. Y. Husseini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.

Lie Algebras And Related Topics

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Author : Georgia Benkart
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Lie Algebras And Related Topics written by Georgia Benkart 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.

Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.

Kazhdan Lusztig Theory And Related Topics

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Author : Vinay Deodhar
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Kazhdan Lusztig Theory And Related Topics written by Vinay Deodhar 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 1992 with Mathematics categories.

This volume attests to the far-reaching influence of Kazhdan-Lusztig theory on several areas of mathematics by presenting a diverse set of research articles centered on this theme. Although there has been a great deal of work in Kazhdan-Lusztig theory, this book is perhaps the first to discuss all aspects of the theory and gives readers a flavor of the range of topics involved. The articles present recent work in Kazhdan-Lusztig theory, including representations of Kac-Moody Lie algebras, geometry of Schubert varieties, intersection cohomology of stratified spaces, and some new topics such as quantum groups.

Clifford Algebras And The Classical Groups

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Author : Ian R. Porteous
language : en
Publisher: Cambridge University Press
Release Date : 1995-10-05

Clifford Algebras And The Classical Groups written by Ian R. Porteous and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-05 with Mathematics categories.

The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G(subscript 2), and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.

A Journey Through Representation Theory

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Author : Caroline Gruson
language : en
Publisher: Springer
Release Date : 2018-10-23

A Journey Through Representation Theory written by Caroline Gruson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-23 with Mathematics categories.

This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.

The Subgroup Structure Of The Finite Classical Groups

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Author : Peter B. Kleidman
language : en
Publisher: Cambridge University Press
Release Date : 1990-04-26

The Subgroup Structure Of The Finite Classical Groups written by Peter B. Kleidman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-26 with Mathematics categories.

With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

Groups Rings Lie And Hopf Algebras

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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-03-31

Groups Rings Lie And Hopf Algebras written by 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 2003-03-31 with Mathematics categories.

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.