[PDF] Centralizers Of Unipotent Elements In Semisimple Algebraic Groups eBook

Author : Ross Lawther
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 36,31 MB
Release : 2011
Category : Mathematics
ISBN : 0821847694

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Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.

Author : Martin W. Liebeck
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 21,7 MB
Release : 2012-01-25
Category : Mathematics
ISBN : 0821869205

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This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.

Author : Ėrnest Borisovich Vinberg
Publisher : American Mathematical Soc.
Page : 284 pages
File Size : 21,90 MB
Release : 2005
Category : Computers
ISBN : 9780821837337

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This volume, devoted to the 70th birthday of A. L. Onishchik, contains a collection of articles by participants in the Moscow Seminar on Lie Groups and Invariant Theory headed by E. B. Vinberg and A. L. Onishchik. The book is suitable for graduate students and researchers interested in Lie groups and related topics.

Author : James E. Humphreys
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 46,98 MB
Release : 1995
Category : Education
ISBN : 0821852760

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Provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.

Author : Jean-Philippe Anker
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 35,70 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 0817681922

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* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

Author : Robert Steinberg
Publisher : American Mathematical Soc.
Page : 628 pages
File Size : 41,6 MB
Release : 1997
Category : Mathematics
ISBN : 9780821805763

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This volume is a collection of published papers by Robert Steinberg. It contains all of his published papers on group theory, including those on "special" representations (now called Steinberg representations), Coxeter groups, regular nilpotent elements and Galois cohomology. After each paper, there is a section, "Comments on the papers", that contains minor corrections and clarifications and explains how ideas and results have evolved and been used since they first appeared.

Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 19,72 MB
Release : 2003
Category : Mathematics
ISBN : 082184377X

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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 : J. S. Milne
Publisher : Cambridge University Press
Page : 665 pages
File Size : 28,94 MB
Release : 2017-09-21
Category : Mathematics
ISBN : 1107167485

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Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.