James E. Humphreys's Books

Representations of Semisimple Lie Algebras in the BGG Category O

By: James E. Humphreys

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Representations of Semisimple Lie Algebras in the BGG Category O

By: James E. Humphreys

This is the first textbook treatment of work leading to the landmark 1979 Kazhdan–Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g g over C C. The setting is the module category O O introduced by Bernstein–Gelfand–Gelfand, which includes all highest weight modules for g g such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of g g. Basic techniques in category O O such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan–Lusztig Conjecture (due to Beilinson–Bernstein and Brylinski–Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: D D-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category O O, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson–Ginzburg–Soergel.

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Page Count

289

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470463261

ISBN 13

9781470463267

Linear Algebraic Groups

By: James E. Humphreys

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Linear Algebraic Groups

By: James E. Humphreys

James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.

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259

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1468494430

ISBN 13

9781468494433

Mansions of Denver

The Vintage Years 1870-1938

By: James Bretz

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Mansions of Denver

The Vintage Years 1870-1938

By: James Bretz

In James Bretz's Mansions of Denver, the charm and history of Denver's architectural past is carefully and beautifully drawn. His book provides readers with insight into the city's youth. But it is also a lament - an homage to a time when architectural originality prevailed.

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Page Count

228

Publisher

Pruett Publishing

Published Date

ISBN 10

0871089378

ISBN 13

9780871089373

Reflection Groups and Coxeter Groups

By: James E. Humphreys

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Reflection Groups and Coxeter Groups

By: James E. Humphreys

This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

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Page Count

222

Publisher

Cambridge University Press

Published Date

ISBN 10

0521436133

ISBN 13

9780521436137

Conjugacy Classes in Semisimple Algebraic Groups

By: James E. Humphreys

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Conjugacy Classes in Semisimple Algebraic Groups

By: James E. Humphreys

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.

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218

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821852760

ISBN 13

9780821852767

Modular Representations of Finite Groups of Lie Type

By: James E. Humphreys

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Modular Representations of Finite Groups of Lie Type

By: James E. Humphreys

A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.

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260

Publisher

Cambridge University Press

Published Date

ISBN 10

0521674549

ISBN 13

9780521674546

Introduction to Lie Algebras and Representation Theory

By: JAMES HUMPHREYS

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Introduction to Lie Algebras and Representation Theory

By: JAMES HUMPHREYS

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.

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Page Count

198

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387900535

ISBN 13

9780387900537

Feigin and Cherry's Textbook of Pediatric Infectious Diseases E-Book

2-Volume Set

By: James Cherry,Gail J. Demmler-Harrison,Sheldon L. Kaplan,William J. Steinbach,Peter J Hotez

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Feigin and Cherry's Textbook of Pediatric Infectious Diseases E-Book

2-Volume Set

By: James Cherry,Gail J. Demmler-Harrison,Sheldon L. Kaplan,William J. Steinbach,Peter J Hotez

Feigin and Cherry's Textbook of Pediatric Infectious Diseases helps you put the very latest knowledge to work for your young patients with unparalleled coverage of everything from epidemiology, public health, and preventive medicine through clinical manifestations, diagnosis, treatment, and much more. Ideal for all physicians, whether in an office or hospital setting, Feigin and Cherry’s equips you with trusted answers to your most challenging clinical infectious disease questions. Meet your most difficult clinical challenges in pediatric infectious disease, including today’s more aggressive infectious and resistant strains as well as emerging and re-emerging diseases, with unmatched, comprehensive coverage of immunology, epidemiology, public health, preventive medicine, clinical manifestations, diagnosis, treatment, and much more. Find the answers you need quickly thanks to an organization both by organ system and by etiologic microorganism, allowing you to easily approach any topic from either direction.

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Page Count

5004

Publisher

Elsevier Health Sciences

Published Date

ISBN 10

0323186602

ISBN 13

9780323186605

Reflection Groups and Coxeter Groups

By: James E. Humphreys

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Reflection Groups and Coxeter Groups

By: James E. Humphreys

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Page Count

222

Publisher

Cambridge University Press

Published Date

ISBN 10

0521436133

ISBN 13

9780521436137

Linear Algebraic Groups

By: James E. Humphreys

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Linear Algebraic Groups

By: James E. Humphreys

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259

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1468494430

ISBN 13

9781468494433

Conjugacy Classes in Semisimple Algebraic Groups

By: James E. Humphreys

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Conjugacy Classes in Semisimple Algebraic Groups

By: James E. Humphreys

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Page Count

218

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821852760

ISBN 13

9780821852767

Book's by James E. Humphreys

Representations of Semisimple Lie Algebras in the BGG Category O

Representations of Semisimple Lie Algebras in the BGG Category O

Linear Algebraic Groups

Linear Algebraic Groups

Mansions of Denver

Mansions of Denver

Reflection Groups and Coxeter Groups

Reflection Groups and Coxeter Groups

Conjugacy Classes in Semisimple Algebraic Groups

Conjugacy Classes in Semisimple Algebraic Groups

Modular Representations of Finite Groups of Lie Type

Modular Representations of Finite Groups of Lie Type

Introduction to Lie Algebras and Representation Theory

Introduction to Lie Algebras and Representation Theory

Feigin and Cherry's Textbook of Pediatric Infectious Diseases E-Book

Feigin and Cherry's Textbook of Pediatric Infectious Diseases E-Book

Reflection Groups and Coxeter Groups

Reflection Groups and Coxeter Groups

Linear Algebraic Groups

Linear Algebraic Groups

Conjugacy Classes in Semisimple Algebraic Groups

Conjugacy Classes in Semisimple Algebraic Groups

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