On Linear Representations of Affine Group 1
Author : Universität München. Mathematisches Institut
Publisher :
Page : 35 pages
File Size : 32,83 MB
Release : 1975
Category :
ISBN :
Author : Universität München. Mathematisches Institut
Publisher :
Page : 35 pages
File Size : 32,83 MB
Release : 1975
Category :
ISBN :
Author : Manfred Bernd Wischnewsky
Publisher :
Page : 35 pages
File Size : 20,76 MB
Release : 1975
Category :
ISBN :
Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 26,19 MB
Release : 2003
Category : Mathematics
ISBN : 082184377X
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.
Author : Manfred Bernd Wischnewsky
Publisher :
Page : 50 pages
File Size : 29,33 MB
Release : 1975
Category : Categories (Mathematics)
ISBN :
Author : W.C. Waterhouse
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 37,31 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461262178
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.
Author : E.B. Vinberg
Publisher : Birkhäuser
Page : 151 pages
File Size : 38,38 MB
Release : 2012-12-06
Category : 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 : Eli Adam Siegel
Publisher :
Page : 244 pages
File Size : 50,42 MB
Release : 1990
Category :
ISBN :
Author : Richard S. Elman
Publisher : American Mathematical Soc.
Page : 215 pages
File Size : 34,15 MB
Release : 1993
Category : Mathematics
ISBN : 0821851616
* 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.
Author : Meinolf Geck
Publisher : Oxford University Press
Page : 321 pages
File Size : 29,16 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 019967616X
An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Author : Roger C. Lyndon
Publisher : Cambridge University Press
Page : 231 pages
File Size : 24,62 MB
Release : 1985-03-14
Category : Mathematics
ISBN : 0521316944
This 1985 book is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and leads the reader to the frontiers of current research at the time of publication.