Character sheaves. III (Q1076805)

The paper under review is part of a series of papers [cf. the author, ibid. 56, 193-237 (1985; Zbl 0586.20018) and 57, 226-265 (1985; Zbl 0586.20019)] devoted to the study of a class \(\hat G\) of irreducible perverse sheaves (called character sheaves) on a connected reductive algebraic group G. One of the main results of the paper reviewed is the following one: under certain assumptions, there is a natural surjective map with finite fibers from \(\hat G\) to the set of all pairs (\({\mathcal L},c)\) (up to conjugacy by the Weyl group), where \({\mathcal L}\) is a tame local system on the maximal torus and c is a ''two-sided cell'' in the stabilizer \(W_{{\mathcal L}}'\) of \({\mathcal L}\) in the Weyl group.