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Sunday, November 1, 2020 | History

12 edition of Modular representation theory found in the catalog.

Modular representation theory

new trends and methods

by David Benson

  • 347 Want to read
  • 21 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Modular representations of groups.,
  • Rings (Algebra)

  • Edition Notes

    StatementDavid Benson.
    SeriesLecture notes in mathematics ;, 1081, Lecture notes in mathematics (Springer-Verlag) ;, 1081.
    Classifications
    LC ClassificationsQA3 .L28 no. 1081, QA171 .L28 no. 1081
    The Physical Object
    Paginationx, 231 p. :
    Number of Pages231
    ID Numbers
    Open LibraryOL2857591M
    ISBN 100387133895
    LC Control Number84020207

    This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne-Lusztig characters.


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Modular representation theory by David Benson Download PDF EPUB FB2

Hi, a very elementary written book is Local Representation Theory by second book on finite groups by Huppert has also a big part about modular representation theory.(you should read the first book too,with an long introduction to representation theory in the semisimple case) a more advanced book is that of feit and a recent () book is "Representations of Groups: A.

The book under review is an introduction to the modular representation theory of finite groups with a somehow balanced approach to the subject. the book is almost self-contained. It has the lightness of a gentle-paced lecture course and could be used with profit for an introduction to the methods of representation theory of finite groups Cited by: The last of these has become a major theme in representation theory Modular representation theory book the 21st century.

Some of this material was incorporated into the author's two-volume Representations and Cohomology, but nevertheless Modular Representation Theory remains a useful by: Modular Representation Theory of finite Groups comprises this second situation. Many additional tools are needed for this case.

Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct. Modular representation theory of finite groups comprises this second Modular representation theory book.

Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. Modular representation theory is the study of representations of groups and related algebras over fields of positive characteristic.

It was initially developed by Brauer, with a view towards the structure of finite groups. Modular Representation Theory of Finite Groups: : Schneider, Peter: Fremdsprachige Bücher. This book provides an accessible introduction to the state of the art of representation theory of finite groups.

Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The representation theory of nite groups has a long history, going back to the 19th This book is about character theory, and it is also Modular representation theory book other things: the character at which point we have modular representations.

In the theory of error-correcting codes many important codes have a non-trivial. Local Representation Theory has 1 rating and 1 review. Steve said: This is a great book on modular representation theory, focusing on the basics J.L.

Alperin. concise treatment of some topics from group theory and representation theory for a one term course. Authors: Alperin, J.L., Bell, Rowen B. Local Structure. Questions about modular representation theory of finite groups can often be reduced to elementary abelian subgroups.

This is the first book to offer a detailed study of the representation theory of elementary abelian groups, bringing together information from many papers and journals, as well as unpublished research. 2 Modular Representation Theory: A First Examination We begin with a brief revision of some previous notions we’ve had in our discussion of representation theory and which results carry over.

Recall: De nition 1. A representation of a group Gover a eld Kis a group homomorphism ˆ: G!GL n(K). The chapter also reviews modular representation theory (p).

By a (p-) modular representation, one means a representation of a group over a field of characteristic p > 0, and a character defined by such a representation is called a modular character.

Some elementary facts on p-modular representations are established in the chapter for a fixed. “This book is intended as a text for first year master students who want to specialize on representation theory, more precisely: representations of finite-dimensional algebras and modular group representations, with special emphasis on homological methods.” (Wolfgang Rump, zbMATH).

The book contains extended versions of seven short lecture courses given during a semester programme on Local Representation Theory and Simple Groups, held at the Centre Interfacultaire Bernoulli of the EPF Lausanne. These courses focused on modular representation theory of finite groups, modern Clifford theoretic methods, the representation.

The last of these has become a major theme in representation theory into the 21st century. Some of this material was incorporated into the author's two-volume Representations and Cohomology, but nevertheless Modular Representation Theory remains a useful introduction.

This book is an outgrowth of a Research Symposium on the Modular Representation Theory of Finite Groups, held at the University of Virginia in May The main themes of this symposium were representations of groups of Lie type in nondefining (or cross) characteristic, and recent developments in block theory.

Series of lectures were given by M. Geck, A. Kleshchev and R. Rouquier, and their. This book is an outgrowth of a Research Symposium on the Modular Representation Theory of Finite Groups, held at the University of Virginia in May The main themes of this symposium were representations of groups of Lie type in nondefining (or cross) characteristic, and recent developments in block theory.

This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1–26 April It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras.

The theory is developed in such a way that almost everything carries over to quantum groups. It emphasizes the similarities between the modular representation theory and the representation theory for quantum groups at roots of unity.

The chapter provides basic general definitions concerning algebraic groups and their representations. Buy G-Algebras and Modular Representation Theory (Oxford Mathematical Monographs) on FREE SHIPPING on qualified orders G-Algebras and Modular Representation Theory (Oxford Mathematical Monographs): Thévenaz, J.: : BooksCited by: Modularity of mind is the notion that a mind may, at least in part, be composed of innate neural structures or mental modules which have distinct, established, and evolutionarily developed functions.

However, different definitions of "module" have been proposed by different authors. According to Fodor, the author of Modularity of Mind, a system can be considered 'modular' if its functions are. The last of these has become a major theme in representation theory into the 21st century.

Some of this material was incorporated into the author's two-volume Representations and Cohomology, but nevertheless Modular Representation Theory remains a useful : Springer-Verlag Berlin Heidelberg.

Modular Lie Algebras and their Representations. Instant. Rewards. Branded. person. A representation of a finite group G over a field k is called modular if the characteristic of k divides the order of G. Many of the basic results in ordinary representation theory are no longer valid in the modular setting (such as complete reducibility), and special techniques are almost certainly required to obtain interesting results, the.

Download Modular Lie Algebras And Their Representations books, This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic.

It introduces the beginner to the theory of modular Lie algebras and is. Modular Representation Theory (New) Lie Theory New modular representation theory connects decomposition numbers for symmetric groups, Hecke algebras, with Lie theory. Idea of “Categorification”: Replace the action of a group or algebra on a vector space by the action of functors on the Grothendieck group of a suitable abelian category.

Frumkin, Avital and Yakir, Arieh Rank of inclusion matrices and modular representation Journal of Mathematics, Vol. 71, Issue.

3, p. This book is an outgrowth of a Research Symposium on the Modular Representation Theory of Finite Groups, held at the University of Virginia in May The main themes of this symposium were representations of groups of Lie type in nondefining (or cross) characteristic, and recent developments in block theory.

It was often the case that, while the conclusions concerned groups of complex matrices, the techniques employed were from modular representation theory.

He also wrote the books: The representation theory of finite groups [2] and Characters of finite groups, [3] which are now standard references on character theory, including treatments of.

'This 2-volume book is a very welcome addition to the existing literature in modular representation theory. It contains a wealth of material much of which is here presented in textbook form for the first time.

It gives an excellent overview of the state of the art in this fascinating subject and also of the many challenging and fundamental. Local Representation Theory book. Read reviews from world’s largest community for readers. Representation theory has applications to number theory, combi 5/5(1).

From the reviews: "The book under review is an introduction to the modular representation theory of finite groups with a somehow balanced approach to the subject.

the book is almost It has the lightness of a gentle-paced lecture course and could be used with profit for an introduction to the methods of representation theory of finite groups. 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, representation.

A BRIEF SUMMARY OF MODULAR REPRESENTATION THEORY 3 This is a particuarly useful result, and one that we would hope in general. How-ever, in the modular case (that is, if p divides the order of G) then this result isn’t true. In fact for any group there will be at least one counter-example.

This can be considered a tropical representation theory, a characteristic one modular representation theory, or a matroidal representation theory—and we draw from all three perspectives.

After some general properties and constructions, including a weak tropical analogue of Maschke's theorem, we turn to a study of the regular representation of. Modular Representation Theory Of Finite And P-adic Groups.

Lecture Notes Series, Institute For Mathematical Sciences, National University Of Singapore (Book 30) Thanks for Sharing. You submitted the following rating and review. We'll publish them on our site once we've reviewed : World Scientific Publishing Company.

This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 thro at Boston University.

Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular. Book. Modular Representation Theory of Finite Groups Details Edited by: Michael J.

Collins, Brian J. Parshall and Leonard L. Scott Edition: Originally published Publisher: De Gruyter. Download file Free Book PDF Local Representation Theory: Modular Representations as an Introduction to the Local Representation Theory of Finite Groups (Cambridge Studies in Advanced Mathematics) at Complete PDF Library.

This Book have some digital formats such us:paperbook, ebook, kindle, epub, fb2 and another formats. Here are two fairly old books that explain and exploit representation theory behind the theory of theta functions and automorphic forms neither assuming nor using algebraic geometry and commutative algebra in a serious way: Gelfand, Graev, Piatetskii-Shapiro, Representation theory and automorphic functions.

Generalized Functions, 6.Local representation theory: modular representations as an introduction to the local representation theory of finite groups. [J L Alperin] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for a beautifully written book.

Anyone wishing to learn the fundamental facts of Brauer's theory of.There are many open problems on modular representation theory of finite groups. There is a well-known list of problems of R. Brauer which date to aroundabout ordinary and modular representations of finite groups. There are other major conjectures (Broue's Abelian defect group conjecture has already been mentioned in comments).