Character sheaves, V

This paper is part of a series [S, 131 devoted to the study of a class G of irreducible perverse sheaves (called character sheaves) on a connected reductive algebraic group G. (The numbering of chapters, sections, and references will continue that of [S, 131.) This paper is a step towards the classification of character sheaves on G. One of the main results is the following one: under certain assumptions, there is a natural surjective map with finite fibers from G to the set of all pairs (9, c) (up to conjugacy by the Weyl group), where 9 is a tame local system on the maximal torus and c is a “two-sided cell’ in the stabilizer W:’ of 9 in the Weyl group. The assumptions made on G are

[1]  G. Lusztig.  Coxeter orbits and eigenspaces of Frobenius , 1976 .

[2]  D. Alvis.  The duality operation in the character ring of a finite Chevalley group , 1979 .

[3]  D. Kazhdan,et al.  Representations of Coxeter groups and Hecke algebras , 1979 .

[4]  G. Lusztig.  Green polynomials and singularities of unipotent classes , 1981 .

[5]  George Lusztig,et al.  Characters of reductive groups over a finite field , 1984 .

[6]  T. Shoji.  On the springer representations of the weyl groups of classical algebraic groups , 1979 .

[7]  W. M. Beynon,et al.  Green functions of finite Chevalley groups of type En (n = 6, 7, 8) , 1984 .

[8]  G. Lusztig,et al.  Representations of reductive groups over finite fields , 1976 .

[9]  P. P. Andre.  $k$-regular elements in semisimple algebraic groups , 1975 .

[10]  G. Lusztig.  Intersection cohomology complexes on a reductive group , 1984 .

[11]  T. A. Springer.  A purity result for fixed point varieties in flag manifolds , 1984 .

[12]  T. A. Springer.  Trigonometric sums, green functions of finite groups and representations of Weyl groups , 1976 .

[13]  G. Lusztig.  Cells in Affine Weyl Groups , 1985 .

[14]  T. Shoji.  On the green polynomials of a chevalley group of type f4 , 1982 .

[15]  P. Deligne.  La conjecture de Weil. I , 1974 .

[16]  G. Lusztig.  Irreducible representations of finite classical groups , 1977 .

[17]  N. Spaltenstein.  On the Generalized Springer Correspondence for Exceptional Groups , 1985 .

[18]  G. Lusztig,et al.  On Springer's correspondence for simple groups of type En (n = 6, 7, 8) , 1982, Mathematical Proceedings of the Cambridge Philosophical Society.

[19]  T. Shoji.  On the Green polynomials of classical groups , 1983 .

[20]  R. Howlett,et al.  Principal series representation of finite groups with split bn pairs , 1980 .

[21]  C. Curtis.  Truncation and duality in the character ring of a finite group of Lie type , 1980 .

[22]  G. Lusztig,et al.  On the Generalized Springer Correspondence for Classical Groups , 1985 .

[23]  G. Lusztig.  Unipotent characters of the symplectic and odd orthogonal groups over a finite field , 1981 .

[24]  Robert Steinberg,et al.  Regular elements of semisimple algebraic groups , 1965 .

[25]  T. Shoji.  Correction to "On the springer representations op the weyl groups of classical algebraic groups" , 1979 .