Reflection Groups And Invariant Theory
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Reflection Groups And Invariant Theory
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Author : Richard Kane
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-21
Reflection Groups And Invariant Theory written by Richard Kane 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 2001-06-21 with Mathematics categories.
Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.
Reflection Groups And Invariant Theory
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Author : Kane
language : en
Publisher: Wiley-Interscience
Release Date : 2003-01-01
Reflection Groups And Invariant Theory written by Kane and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with categories.
Reflection Groups And Invariant Theory
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Author :
language : en
Publisher:
Release Date : 2011
Reflection Groups And Invariant Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Reflection Groups And Coxeter Groups
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Author : James E. Humphreys
language : en
Publisher: Cambridge University Press
Release Date : 1992-10
Reflection Groups And Coxeter Groups written by James E. Humphreys 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 1992-10 with Mathematics categories.
This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.
Invariant Theory Of Finite Groups
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Author : Mara D. Neusel
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Invariant Theory Of Finite Groups written by Mara D. Neusel 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 2002 with Mathematics categories.
The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods andtools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invarianttheory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, ad The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader withorientation to the vast literature.
Multiplicative Invariant Theory
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Author : Martin Lorenz
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-10
Multiplicative Invariant Theory written by Martin Lorenz 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 2005-03-10 with Mathematics categories.
Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori. Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2. The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.
Finite Reflection Groups
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Author : L.C. Grove
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-06-20
Finite Reflection Groups written by L.C. Grove 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 1996-06-20 with Mathematics categories.
Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude.
Unitary Reflection Groups
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Author : Gustav I. Lehrer
language : en
Publisher: Cambridge University Press
Release Date : 2009-08-13
Unitary Reflection Groups written by Gustav I. Lehrer 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 2009-08-13 with Mathematics categories.
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.
Computational Invariant Theory
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Author : Harm Derksen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Computational Invariant Theory written by Harm Derksen 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 2013-04-17 with Mathematics categories.
Invariant theory is a subject with a long tradition and an astounding abil ity to rejuvenate itself whenever it reappears on the mathematical stage. Throughout the history of invariant theory, two features of it have always been at the center of attention: computation and applications. This book is about the computational aspects of invariant theory. We present algorithms for calculating the invariant ring of a group that is linearly reductive or fi nite, including the modular case. These algorithms form the central pillars around which the book is built. To prepare the ground for the algorithms, we present Grabner basis methods and some general theory of invariants. Moreover, the algorithms and their behavior depend heavily on structural properties of the invariant ring to be computed. Large parts of the book are devoted to studying such properties. Finally, most of the applications of in variant theory depend on the ability to calculate invariant rings. The last chapter of this book provides a sample of applications inside and outside of mathematics.
Lectures On Invariant Theory
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Author : Igor Dolgachev
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-07
Lectures On Invariant Theory written by Igor Dolgachev 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 2003-08-07 with Mathematics categories.
The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.