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Saturday, April 25, 2020 | History

8 edition of Representations of algebraic groups found in the catalog.

Representations of algebraic groups

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  • 3 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Representations of groups,
  • Linear algebraic groups

  • Edition Notes

    Includes bibliographical references and index.

    StatementJens Carsten Jantzen.
    SeriesMathematical surveys and monographs,, v. 107, Mathematical surveys and monographs ;, no. 107.
    Classifications
    LC ClassificationsQA176 .J37 2003
    The Physical Object
    Paginationxiii, 576 p. :
    Number of Pages576
    ID Numbers
    Open LibraryOL3689894M
    ISBN 100821835270
    LC Control Number2003058381


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Representations of algebraic groups by Jens Carsten Jantzen Download PDF EPUB FB2

The book is suitable for graduate students and research mathematicians interested in algebraic groups and their representations. Algebra, as a subdiscipline of mathematics, arguably has a history going back some years to ancient history, however, of what is recognized today as high school algebra is much shorter, extending Cited by:   It continues to be the ultimate source of information on representations of algebraic groups in finite characteristics.

The book is suitable for graduate students and research mathematicians interested in algebraic groups and their representations.

Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics Book ) - Kindle edition by Hall, Brian. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate /5(16).

The second part of the book is devoted to the representation theory of reductive algebraic groups and Representations of algebraic groups book topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's Representations of algebraic groups book formula, and.

theory of such groups as the general linear groups GL n(k), the special linear groups SL n(k), the special orthogonal groups SO n(k), and the symplectic groups Sp2 n(k) over an algebraically closed field k.

These Representations of algebraic groups book are algebraic groups, and we shall look only at representations G —> GL(V) that are homomorphisms of algebraic groups. Get this from Representations of algebraic groups book library.

Representations of algebraic groups. [Jens Carsten Jantzen] -- "The present book, which is a revised edition of the author's book published in by Academic Press, is intended to give the reader an introduction to.

This revised edition of the monograph (originally published by Academic Press) provides an introduction to the theory of algebraic representations of reductive algebraic groups. Jantzen (mathematics, East China University in Shanghai) begins by outlining a general theory of representations of a Read more.

Algebraic Groups The theory of group schemes of finite type over a field. J.S. Milne Version Decem This is a rough preliminary version of the book published by CUP inThe final Representations of algebraic groups book is substantially rewritten, and the numbering has changed.

The Mathematical Sciences Research Institute (MSRI), founded inis an independent nonprofit Representations of algebraic groups book research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions.

The Representations of algebraic groups book is located at 17 Gauss Way, on the University of California, Berkeley campus, close to. thereby giving representations of the group on the homology groups of the space. If there is torsion in the homology these representations require something other than ordinary character theory to be understood.

This book is written for students who are studying nite group representation theory beyond the level of a rst course in abstract Size: 1MB.

Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic by: The first Representations of algebraic groups book I read on algebraic groups was An Introduction to Algebraic Geometry and Algebraic Groups by Meinolf Geck.

As I recall, the book includes a lot of examples about the classical matrix groups, and gives elementary accounts of such things like computing the tangent space at the identity to get the Lie algebra. The second part of the book is devoted to the representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and line bundles on them.

This is a significantly revised edition of a modern classic. The second part of the book is devoted to the representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and line bundles on : Jens Carsten Jantzen.

$\begingroup$ @Joao: Your question may involve more number theory than algebraic groups (in which case a tag '-theory' might be helpful). One possible dividing line is the fact that the structure and representations of a given algebraic group or group-scheme over a field of prime characteristic tend to behave uniformly over an arbitrary algebraically closed field of that.

The chapter provides basic general definitions concerning algebraic groups and their representations. In addition, it also proves the Borel-Weil-Bott theorem and Serre duality. From these two results it is easily deduced the complete reducibility of all finite dimensional modules for algebraic groups in characteristic zero.

(source: Nielsen Book Data) Summary Now back in print by the AMS, this is a significantly revised edition of a book originally published in by Academic Press. This book gives the reader an introduction to the theory of algebraic representations of reductive algebraic groups. The representation theory of linear algebraic groups and Lie groups extends these examples to infinite-dimensional groups, the latter being intimately related to Lie algebra representations.

The importance of character theory for finite groups has an analogue in the theory of weights for representations of Lie groups and Lie algebras. Part of the Lecture Notes in Mathematics book series (LNM, volume ) Log in to check access.

Buy eBook. The classical groups. Stephen Donkin. Pages Homological algebra revisited. Stephen Donkin. Pages G 2. Stephen Donkin. Group algebra algebraic group filtration homological algebra presentation.

Bibliographic information. Algebraic Geometry *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook : Springer-Verlag Berlin Heidelberg.

This volume contains invited articles by top-notch experts who focus on such topics as: modular representations of algebraic groups, representations of quantum groups and crystal bases, representations of affine Lie algebras, representations of affine Hecke algebras, modular or ordinary representations of finite reductive groups, and representations of complex reflection.

This book contains the proceedings of the Conference on Linear Algebraic Groups and Their Representations, held at UCLA in March The central theme is the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics.

Representations of Algebraic Groups: Second Edition. Set up a giveaway. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes. This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites.

In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on.

This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al­ gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to.

This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al­ gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July The Lie algebra of an algebraic group.

Notes. Exercises. Oct Representations of SL 2 and sl 2. You should now also start reading Fulton-Harris, especially Chapter Notes. Exercises. Oct Solvable and nilpotent Lie algebras. Reading material: the Fulton-Harris book, sections andand/or the book by Humphreys, Chapter 3.

Destination page number Search scope Search Text Search scope Search Text. Purchase Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Volume 1 - 1st Edition. Print Book & E-Book. ISBNGeometric Group Theory Preliminary Version Under revision.

The goal of this book is to present several central topics in geometric group theory, primarily related to the large scale geometry of infinite groups and spaces on which such groups act, and to illustrate them with fundamental theorems such as Gromov’s Theorem on groups of polynomial growth.

$\begingroup$ I mean, you really just want to know the theory of dominant weights for reductive algebraic groups. You should see Milne's notes. There are a veritable cornucopia of resources to study representations of algebraic groups. As to your second question the answer is--it depends.

I am reading some lie groups/lie algebras on my own. I am using Brian Hall's Lie Groups, Lie Algebras, and Representations: An Elementary Introduction. I was checking for some other references on lie groups and found J.

Milne's notes Lie Algebras, Algebraic Groups,and Lie Groups. It was written in introductory page of algebraic groups chapter that. There are a number of analogous results between algebraic groups and Coxeter groups – for instance, the number of elements of the symmetric group is!, and the number of elements of the general linear group over a finite field is the q-factorial []!; thus the symmetric group behaves as though it were a linear group over "the field with one element".

The book contains several well-written, accessible survey papers in many interrelated areas of current research.

These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. Representations of Algebraic Groups: Jens Carsten Jantzen: This is an authoritative [book] which, in its updated form, will continue to be the research worker’s main reference.

Thank God and the AMS that this book is back in print, it is the sacred word for anyone in this field, and the new appendix covers many new developments since the. The book is expertly written, though the reader should be warned that it is not meant to be self-contained; J.C. Jantzen's Representations of Algebraic Groups is the standard reference for this material.

As usual, his bibliography is compiled with great care and contains references that "may not turn up readily in a MathSciNet search". Back in print from the AMS, the first part of this book is an introduction to the general theory of representations of algebraic group schemes. Here, Janzten.

Now back in print by the AMS, this is a significantly revised edition of a book originally published in by Academic Press. This book gives the reader an.

Donkin, Stephen. Universal classes for algebraic groups Touzé, Antoine, Duke Mathematical Journal, ; Quantum representations of braid groups and holonomy Lie algebras Kohno, Toshitake, ; Deformations with respect to an algebraic group Bleher, Frauke M. and Chinburg, Ted, Illinois Journal of Mathematics, ; Cuntz-Pimsner algebras of group Cited by: Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties.

The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of. See Representations of Lie groups and Representations of Lie algebras.

Linear algebraic groups (or more generally affine group schemes) — These are the analogues of Lie groups, but over more general fields than just R or C.

Although linear algebraic groups have a classification that is very similar to that of Lie groups, and give rise to the. v ( ; pages). Posted pdf Algebraic Groups and Arithmetic Groups (AAG). v (Ap ; pages). First version of expanded notes (first two chapters only). Posted as Algebraic Groups, Lie Groups, and their Arithmetic Subgroups (ALA).

v (Ap ; pages). Posted new version of all six chapters.The linear algebraic download pdf I study may all be viewed as collections of linear symmetries of a vector space; a linear representation -- or a module -- is (roughly speaking) a choice of such a vector space.

Representations thus provide a practical tool -- linear algebra -- for studying the abstract, algebraic notion of a group.Additional Sources for Math Book Reviews; About MAA Reviews; Mathematical Ebook Information for Libraries; Author Resources; Advertise with MAA; Meetings.

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