 
Summary: .
NAGOYA MATHEMATICAL JOURNAL, VOL 170, TO APPEAR IN JUNE 2003
CHARACTER SHEAVES AND GENERALIZED SPRINGER
CORRESPONDENCE
ANNEMARIE AUBERT
Abstract. Let G be a connected reductive algebraic group over an algebraic
closure of a finite field of characteristic p. Under the assumption that p is
good for G, we prove that for each character sheaf A on G which has nonzero
restriction to the unipotent variety of G, there exists a unipotent class CA
canonically attached to A, such that A has nonzero restriction on CA , and
any unipotent class C in G on which A has nonzero restriction has dimension
strictly smaller than that of CA .
1. Introduction
Let F q be an algebraic closure of a finite field F q of q elements. Let G be a
connected reductive algebraic group over F q , defined over F q . Let T be a maximal
torus in G, T \Lambda be a maximal torus in the Langlands dual G \Lambda of G which is dual
to T , and let W = W G denote the Weyl group of G with respect to T , that we
identify with the Weyl group of G \Lambda with respect to T \Lambda . Let s 2 T \Lambda . Lusztig has
defined a canonical surjective map from the set “
G of characters sheaves on G to the
