Representation theory of finite reductive groups / Marc Cabanes, Michel Enguehard.

Format:

Book

Author/Creator:

Cabanes, Marc, 1959- author.

Enguehard, Michel, author.

Series:

New mathematical monographs ; 1.

New mathematical monographs ; 1

Language:

English

Subjects (All):

Finite groups.

Representations of groups.

Physical Description:

1 online resource (xvii, 436 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2004.

Language Note:

English

Summary:

At the crossroads of representation theory, algebraic geometry and finite group theory, this 2004 book blends together many of the main concerns of modern algebra, with full proofs of some of the most remarkable achievements in the area. Cabanes and Enguehard follow three main themes: first, applications of étale cohomology, leading to the proof of the recent Bonnafé-Rouquier theorems. The second is a straightforward and simplified account of the Dipper-James theorems relating irreducible characters and modular representations. The final theme is local representation theory. One of the main results here is the authors' version of Fong-Srinivasan theorems. Throughout the text is illustrated by many examples and background is provided by several introductory chapters on basic results and appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and reference for all algebraists.

Contents:

pt. I. Representing Finite BN-Pairs

1. Cuspidality in finite groups

2. Finite BN-pairs

3. Modular Hecke algebras for finite BN-pairs

4. The modular duality functor and derived category

5. Local methods for the transversal characteristics

6. Simple modules in the natural characteristic

pt. II. Deligne-Lusztig Varieties, Rational Series, and Morita Equivalences

7. Finite reductive groups and Deligne -Lusztig varieties

8. Characters of finite reductive groups

9. Blocks of finite reductive groups and rational series

10. Jordan decomposition as a Morita equivalence: the main reductions

11. Jordan decomposition as a Morita equivalence: sheaves.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 422-430) and index.

ISBN:

1-107-14660-7

1-280-43741-3

9786610437412

0-511-18413-1

0-511-16566-8

0-511-16373-8

0-511-31267-9

0-511-54276-3

0-511-16453-X

OCLC:

171138182