On Linear Representations Of Affine Groups
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On Linear Representations Of Affine Groups
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Author : Manfred Bernd Wischnewsky
language : en
Publisher:
Release Date : 1975
On Linear Representations Of Affine Groups written by Manfred Bernd Wischnewsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Categories (Mathematics) categories.
Introduction To Affine Group Schemes
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Author : W.C. Waterhouse
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Affine Group Schemes written by W.C. Waterhouse 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 2012-12-06 with Mathematics categories.
Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.
Linear Representations Of Groups
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Author : E.B. Vinberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Linear Representations Of Groups written by E.B. Vinberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Linear Algebraic Groups And Their Representations
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Author : Richard S. Elman
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Linear Algebraic Groups And Their Representations written by Richard S. Elman 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 1993 with Mathematics categories.
* Brings together a wide variety of themes under a single unifying perspective The proceedings of a conference on Linear algebraic Groups and their Representations - the text gets to grips with the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics.
Representations Of Algebraic Groups
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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Representations Of Algebraic Groups written by Jens Carsten Jantzen 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 2003 with Mathematics categories.
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
The Classical Groups
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Author : Hermann Weyl
language : en
Publisher: Princeton University Press
Release Date : 1946
The Classical Groups written by Hermann Weyl and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1946 with Mathematics categories.
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.
Linear Algebra And Group Representations Linear Algebra And Introduction To Group Representations
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Author : Ronald Shaw
language : en
Publisher:
Release Date : 1982
Linear Algebra And Group Representations Linear Algebra And Introduction To Group Representations written by Ronald Shaw and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Quantum Linear Groups And Representations Of Gl N Mathbb F Q
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Author : Jonathan Brundan
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Quantum Linear Groups And Representations Of Gl N Mathbb F Q written by Jonathan Brundan 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 2001 with Mathematics categories.
We give a self-contained account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL[n(F[q) over fields of characteristic coprime to q to the representation theory of "quantum GL[n" at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL[n and Harish-Chandra induction in finite GL[n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition for p-singular classes. From that we obtain simplified treatments of various basic known facts, such as the computation of decomposition numbers and blocks of GL[n(F[q) from knowledge of the same for the quantum group, and the non-defining analogue of Steinberg's tensor product theorem. We also easily obtain a new double centralizer property between GL[n(F[[q) and quantum GL[n, generalizing a result of Takeuchi. Finally, we apply the theory to study the affine general linear group, following ideas of Zelevinsky in characteristic zero. We prove results that can be regarded as the modular analogues of Zelevinsky's and Thoma's branching rules. Using these, we obtain a new dimension formula for the irreducible cross-characteristic representations of GL[n(F[q), expressing their dimensions in terms of the characters of irreducible modules over the quantum group.
Representations Of Finite Classical Groups
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Author : A. V. Zelevinsky
language : en
Publisher: Springer
Release Date : 2006-11-14
Representations Of Finite Classical Groups written by A. V. Zelevinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Linear Representations Of Groups
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Author : Ėrnest Borisovich Vinberg
language : en
Publisher: Birkhauser
Release Date : 1989
Linear Representations Of Groups written by Ėrnest Borisovich Vinberg and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.