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.

George Lusztig

• Frontmatter,
• TABLE OF CONTENTS,
• INTRODUCTION,
• 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY,
• 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW,
• 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X¯W,
• 4. REPRESENTATIONS OF WEYL GROUPS,
• 5. CELLS IN WEYL GROUPS,
• 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM,
• 7. SOME EXCEPTIONAL GROUPS,
• 8. DECOMPOSITION OF INDUCED REPRESENTATIONS,
• 9. CLASSICAL GROUPS,
• 10. COMPLETION OF THE PROOF OF THEOREM 4.23,
• 11. EIGENVALUES OF FROBENIUS,
• 12. ON THE STRUCTURE OF LEFT CELLS,
• 13. RELATIONS WITH CONJUGACY CLASSES,
• 14. CONCLUDING REMARKS,
• APPENDIX,
• REFERENCES,
• SUBJECT INDEX,
• NOTATION INDEX,
• Backmatter,