Characters of Reductive Groups over a Finite Field PDF
Preview Characters of Reductive Groups over a Finite Field
Annals of Mathematics Studies Number 107 CHARACTERS OF REDUCTIVE GROUPS OVER A FINITE FIELD BY GEORGE LUSZTIG PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY 1984 Copyright © 1984 by Princeton University Press ALL RIGHTS RESERVED The Annals of Mathematics Studies are edited by William Browder, Robert P. Langlands, John Milnor, and Elias M. Stein Corresponding editors: Stefan Hildebrandt, H. Blaine Lawson, Louis Nirenberg, and David Vogan Clothbound editions of Princeton University Press books are printed on acid-free paper, and binding materials are chosen for strength and durability. Pa perbacks, while satisfactory for personal collections, are not usually suitable for library rebinding ISBN 0-691-08350-9 (cloth) ISBN 0-691-08351-7 (paper) Printed in the United States of America by Princeton University Press, 41 William Street Princeton, New Jersey Library of Congress Cataloging in Publication data will be found on the last printed page of this book To Miki, Irene and Tamar TABLE OF CONTENTS INTRODUCTION ix 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY 3 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES xw 30 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY Xw 58 4. REPRESENTATIONS OF WEYL GROUPS 76 5. CELLS IN WEYL GROUPS 134 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM 180 7. SOME EXCEPTIONAL GROUPS 217 8. DECOMPOSITION OF INDUCED REPRESENTATIONS 251 9. CLASSICAL GROUPS 269 10. COMPLETION OF THE PROOF OF THEOREM 4.23 296 11. EIGENVALUES OF FROBENIUS 313 12. ON THE STRUCTURE OF LEFT CELLS 324 13. RELATIONS WITH CONJUGACY CLASSES 342 14. CONCLUDING REMARKS 351 APPENDIX 358 REFERENCES 377 SUBJECT INDEX 382 NOTATION INDEX 383 vii
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