Representations of Finite Chevalley Groups A Survey
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764 Bhama Srinivasan
Representations of Finite Chevalley Groups A Survey
Springer-Verlag Berlin Heidelberg New York 1979
Author B h a m a Srinivasan D e p a r t m e n t of M a t h e m a t i c s C l a r k University W o r c e s t e r , M a s s a c h u s e t t s 01610 USA
A M S S u b j e c t C l a s s i f i c a t i o n s (1970): 2 0 C 1 5 , 2 0 G 4 0 ISBN 3 - 5 4 0 - 0 9 7 1 6 - 3 S p r i n g e r - V e r l a g Berlin H e i d e l b e r g N e w Y o r k ISBN 0 - 3 8 7 - 0 9 7 1 6 - 3 S p r i n g e r - V e r l a g N e w Y o r k H e i d e l b e r g Berlin Library of Congress Cataloging in Publication Data Srinivasan, Bhama, 1935Representations of finite Chevalley groups. (Lecture notes in mathematics; 764) Bibliography: p. Includes index. 1. Chevalley groups. 2. Finite groups. 3. Representations of groups. I. Title. II. Series: Lecture notes in mathematics (Berlin); 764. QA3.L28 no. 764 [QA171] 510'.8s [512'.22] 79-26526 ISBN 0-387-09716-3 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks, Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher, © by Springer-Verlag Berlin Heidelberg 1979 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
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INTRODUCTION The
aim of these
developments
in the theory
representations in recent groups
notes
of finite
years.
arising
for A d v a n c e d
Chevalley
In the year
In this
on H a r i s h - C h a n d r a ' s
at that
time been applied
that
there
the so called
groups seminar
also
was held T.A.
would be families
on finite
at the Institute
Springer
finite
gave
of the various
An i m p o r t a n t
breakthrough
in 1976 w h e n L u s z t l g
[183
by
constructing
£-adic
cohomology
of c e r t a i n
An outline
of the contents
a review theory" closed
field.
the s i t u a t i o n
defined
over
of
The group
group whose
~q,
problem
tori
"maximal
~roups
tori ~.
and D e l i E n e
of these
conjectures,
of the groups
on the
is as follows.
that we need groups
II and
Chapter
on the
I is
"absolute
over an a l g e b r a i c a l l y
in the rest of the notes we
where
O
is a connected
reductive
and where
F
is a F r o b e n l u s
endomorphlsm
GF
of fixed points
representation
of the m a x i m a l
predleted
varieties.
algebraic
In C h a p t e r
a proof
representations
of the m a i n results of reductlve
consider
O.
virtual
published
Sprln~er
of these
by the characters
paper
which had
which
parametrized
in their famous
some
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came
of
of c o n s t r u c t i n g
GF
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