Complete reducibility, Külshammer's question, conjugacy classes: A D4 example
Let k be a nonperfect separably closed field. Let G be a connected reductive algebraic group defined over k. We study rationality problems for Serre's notion of complete reducibility of subgroups of G. In particular, we present a new example of subgroup H of G of type D4 in characteristic 2 suc...
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| Published in | Communications in algebra Vol. 46; no. 3; p. 1333 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Abingdon
Taylor & Francis Ltd
04.03.2018
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| Subjects | |
| Online Access | Get full text |
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| Summary: | Let k be a nonperfect separably closed field. Let G be a connected reductive algebraic group defined over k. We study rationality problems for Serre's notion of complete reducibility of subgroups of G. In particular, we present a new example of subgroup H of G of type D4 in characteristic 2 such that H is G-completely reducible but not G-completely reducible over k (or vice versa). This is new: all known such examples are for G of exceptional type. We also find a new counterexample for Külshammer's question on representations of finite groups for G of type D4. A problem concerning the number of conjugacy classes is also considered. The notion of nonseparable subgroups plays a crucial role in all our constructions. |
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| ISSN: | 0092-7872 1532-4125 |
| DOI: | 10.1080/00927872.2017.1346106 |