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Character sheaves. III. (English) Zbl 0594.20031

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.
Reviewer: N.I.Osetinski

MSC:

20G05 Representation theory for linear algebraic groups
14F30 \(p\)-adic cohomology, crystalline cohomology
14L30 Group actions on varieties or schemes (quotients)
20G15 Linear algebraic groups over arbitrary fields
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References:

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