03527 - Representation Theory of Finite Reductive Groups.pdf

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Representation Theory of Finite Reductive Groups
At the crossroads of representation theory, algebraic geometry and finite group theory,
this book blends together many of the main concerns of modern algebra, synthesizing
the past 25 years of research, with full proofs of some of the most remarkable
achievements in the area.
Cabanes and Enguehard follow three main themes: first, applications of etale
´
cohomology, leading, via notions of twisted induction, unipotent characters and
Lusztig’s approach to the Jordan decomposition of characters, to the proof of the
recent Bonnaf´ –Rouquier theorems. The second is a straightforward and simplified
e
account of the Dipper–James theorems relating irreducible characters and modular
representations, while introducing modular Hecke and Schur algebras. The final theme
is local representation theory. One of the main results here is the authors’ version of
Fong–Srinivasan theorems showing the relations between twisted induction and blocks
of modular representations.
Throughout, the text is illustrated by many examples; 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.
m a r c c a b a n e s
is Charg´ de Recherche at Universit´ Paris 7
e
e
m i c h e l e n g u e h a r d
is Professeur Em´ rite, Universit´ Paris 8.
e
e
New Mathematical Monographs
Editorial Board
B´ la Bollob´ s,
University of Memphis
e
a
William Fulton,
University of Michigan
Frances Kirwan,
Mathematical Institute, University of Oxford
Peter Sarnak,
Princeton University
Barry Simon,
California Institute of Technology
For information about Cambridge University Press mathematics publications visit
http://publishing.cambridge.org/stm/mathematics/
Representation Theory of Finite
Reductive Groups
MARC CABANES, MICHEL ENGUEHARD
Universit´ Paris
e
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge
cb2 2ru,
UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521825177
© Cambridge University Press 2004
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2004
isbn-13
isbn-10
isbn-13
isbn-10
978-0-511-16566-5
eBook (NetLibrary)
0-511-16566-8
eBook (NetLibrary)
978-0-521-82517-7
hardback
0-521-82517-2
hardback
Cambridge University Press has no responsibility for the persistence or accuracy of
urls
for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.

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