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- Publisher Website: 10.1016/j.jalgebra.2017.04.018
- Scopus: eid_2-s2.0-85019368589
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Article: Lifting of elements of Weyl groups
Title | Lifting of elements of Weyl groups |
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Authors | |
Keywords | Algebraic groups Tits group Weyl groups |
Issue Date | 2017 |
Citation | Journal of Algebra, 2017, v. 485, p. 142-165 How to Cite? |
Abstract | Suppose G is a reductive algebraic group, T is a Cartan subgroup of G, N=Norm(T), and W=N/T is the Weyl group. If w∈W has order d, it is natural to ask about the orders lifts of w to N. It is straightforward to see that the minimal order of a lift of w has order d or 2d, but it can be a subtle question which holds. We first consider the question of when W itself lifts to a subgroup of N (in which case every element of W lifts to an element of N of the same order). We then consider two natural classes of elements: regular and elliptic. In the latter case all lifts of w are conjugate, and therefore have the same order. We also consider the twisted case. |
Persistent Identifier | http://hdl.handle.net/10722/329442 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 1.023 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Adams, Jeffrey | - |
dc.contributor.author | He, Xuhua | - |
dc.date.accessioned | 2023-08-09T03:32:49Z | - |
dc.date.available | 2023-08-09T03:32:49Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Journal of Algebra, 2017, v. 485, p. 142-165 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | http://hdl.handle.net/10722/329442 | - |
dc.description.abstract | Suppose G is a reductive algebraic group, T is a Cartan subgroup of G, N=Norm(T), and W=N/T is the Weyl group. If w∈W has order d, it is natural to ask about the orders lifts of w to N. It is straightforward to see that the minimal order of a lift of w has order d or 2d, but it can be a subtle question which holds. We first consider the question of when W itself lifts to a subgroup of N (in which case every element of W lifts to an element of N of the same order). We then consider two natural classes of elements: regular and elliptic. In the latter case all lifts of w are conjugate, and therefore have the same order. We also consider the twisted case. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Algebra | - |
dc.subject | Algebraic groups | - |
dc.subject | Tits group | - |
dc.subject | Weyl groups | - |
dc.title | Lifting of elements of Weyl groups | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.jalgebra.2017.04.018 | - |
dc.identifier.scopus | eid_2-s2.0-85019368589 | - |
dc.identifier.volume | 485 | - |
dc.identifier.spage | 142 | - |
dc.identifier.epage | 165 | - |
dc.identifier.eissn | 1090-266X | - |
dc.identifier.isi | WOS:000403626000006 | - |