Restriction of a character sheaf to conjugacy classes
Let A be a character sheaf on a connected reductive 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...
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| Format: | Article |
| Language: | en_US |
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Societatea de Ştiinţe Matematice din România
2016
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| Online Access: | http://hdl.handle.net/1721.1/105143 https://orcid.org/0000-0001-9414-6892 |
| Summary: | Let A be a character sheaf on a connected reductive 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 of G in terms of restriction to conjugacy classes. Without restriction on characteristic we define canonical bijections from the set of unipotent representations of the corresponding split group over a finite field to a set combinatorially defined in terms of the Weyl group. |
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