Characters of Reductive Groups over a Finite Field

by George Lusztig

Overview

This book presents a classification of all (complex)
irreducible representations of a reductive group with connected centre, over a finite field. To achieve this,
the author uses etale intersection cohomology, and detailed information on representations of Weyl groups.

Product Details

ISBN-13:	9780691083513
Publisher:	Princeton University Press
Publication date:	06/21/1984
Series:	Annals of Mathematics Studies , #107
Pages:	408
Product dimensions:	6.00(w) x 9.00(h) x (d)

Table of Contents

• Frontmatter, pg. i
• TABLE OF CONTENTS, pg. vii
• INTRODUCTION, pg. ix
• 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY, pg. 1
• 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW, pg. 30
• 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X̅W, pg. 58
• 4. REPRESENTATIONS OF WEYL GROUPS, pg. 76
• 5. CELLS IN WEYL GROUPS, pg. 134
• 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM, pg. 180
• 7. SOME EXCEPTIONAL GROUPS, pg. 217
• 8. DECOMPOSITION OF INDUCED REPRESENTATIONS, pg. 251
• 9. CLASSICAL GROUPS, pg. 269
• 10. COMPLETION OF THE PROOF OF THEOREM 4.23, pg. 296
• 11. EIGENVALUES OF FROBENIUS, pg. 313
• 12. ON THE STRUCTURE OF LEFT CELLS, pg. 324
• 13. RELATIONS WITH CONJUGACY CLASSES, pg. 342
• 14. CONCLUDING REMARKS, pg. 351
• APPENDIX, pg. 358
• REFERENCES, pg. 377
• SUBJECT INDEX, pg. 382
• NOTATION INDEX, pg. 383
• Backmatter, pg. 385