Seminar on Algebraic Groups and Related Finite Groups Held at The In
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131 A. Borel R. Carter C.W Curtis N.lwahori T. A. Springer R. Steinberg
Seminar on Algebraic Groups and Related Finite Groups Held at The Institute for Advanced Study Princeton/NJ, 1968/69
Springer-Verlag Berlin Heidelberg New York Tokyo
Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann Subseries: Mathematisches Institut der Universitat Bonn Adviser: F. Hirzebruch
131 A. Borel R. Carter C.W Curtis N.lwahori T. A. Springer R. Steinberg
Seminar on Algebraic Groups and Related Finite Groups Held at The Institute for Advanced Study Princeton/NJ, 1968/69
Springer-Verlag Berlin Heidelberg New York Tokyo
Authors Armand Borel Forschungsinstitut fur Mathematik, ETH Zentrum 8092 Zurich, Switzerland RW. Carter Mathematics Institute, University of Warwick Coventry CV4 7AL, England Charles W. Curtis University of Oregon, Dept. of Mathematics Eugene, OR 97403, USA Nagayoshi Iwahori Dept. of Mathematics, Faculty of Science University of Tokyo Hongo, Tokyo 113, Japan T. A. Springer Dept. of Mathematics, Rijksuniversiteit Utrecht Budapestlaan 6, Postbus 80.010 3508 TA Utrecht, The Netherlands Robert Steinberg Dept. of Mathematics, University of California Los Angeles, CA 90024, USA
1st Edition 1970 2nd Corrected Printing 1986
Mathematics Subject Classification (1980): 20-xx; 14L ISBN 3-540-04920-7 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-04920-7 Springer-Verlag New York Heidelberg Berlin Tokyo
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INTRODUCTION
This volume contains the Notes of a seminar held at the Institute in 1968 -69, in the framework of a program on linear algebraic groups and finite groups. (':,) They emphasize a borderline topic between these two topics: the linear representations, both modular and over the complex numbers, of the finite Chevalley groups and of some generalizations of them.
They also contain a discussion of some questions on
algebraic groups which are both relevant to the main theme and of independent interest. Part A first supplies some background material:
construction
and main properties of Chevalley groups over a field or over
and
of rational representations of a semi-simple algebraic group over an algebraically closed groundfield.
It then turns to results of Curtis
and Steinberg describing the representations of a Chevalley group over a field of non-zero characteristic whose differential is also irreducible, and the construction of the irreducible representations of the group by means of them.
As far as the finite Chevalley
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