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arXiv · 1204.3521

Restriction of a character sheaf to conjugacy classes

G. Lusztig
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Abstract

Let A be a character sheaf on a reductive connected group G over an algebraically closed field. Assuming that the characteristic is not bad, we show that for certain conjugacy classes D in G the restriction of A to D is a local system up to shift; we also give a parametrization of unipotent cuspidal character sheaves on G in terms of restrictions to conjugacy classes. Without restriction on characteristic we define canonical bijections from the set of unipotent character sheaves on G (and from the set of unipotent representations of the corresponding split reductive group over a finite field) to a set combinatorially defined in terms of the Weyl group.

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G. Lusztig. 2012-06-21. Restriction of a character sheaf to conjugacy classes. https://arxiv.org/abs/1204.3521

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