Splitting fields of real irreducible representations of finite groups
<p>We show that any irreducible representation ρ of a finite group G of exponent n, realisable over R, is realisable over the field E:= Q(ζn) ∩ R of real cyclotomic numbers of order n, and describe an algorithmic procedure transforming a reali...
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| Format: | Journal article |
| Language: | English |
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American Mathematical Society
2021
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| _version_ | 1797102997041315840 |
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| author | Pasechnik, DV |
| author_facet | Pasechnik, DV |
| author_sort | Pasechnik, DV |
| collection | OXFORD |
| description | <p>We show that any irreducible representation ρ of a finite group G of exponent n, realisable over R, is realisable over the field E:= Q(ζn) ∩ R of real cyclotomic numbers of order n, and describe an algorithmic procedure transforming a realisation of ρ over Q(ζn) to one over E.</p> |
| first_indexed | 2024-03-07T06:13:45Z |
| format | Journal article |
| id | oxford-uuid:f067f178-b5d9-44dd-9897-8b5e322f7e9a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:13:45Z |
| publishDate | 2021 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:f067f178-b5d9-44dd-9897-8b5e322f7e9a2022-03-27T11:47:39ZSplitting fields of real irreducible representations of finite groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f067f178-b5d9-44dd-9897-8b5e322f7e9aEnglishSymplectic ElementsAmerican Mathematical Society2021Pasechnik, DV<p>We show that any irreducible representation ρ of a finite group G of exponent n, realisable over R, is realisable over the field E:= Q(ζn) ∩ R of real cyclotomic numbers of order n, and describe an algorithmic procedure transforming a realisation of ρ over Q(ζn) to one over E.</p> |
| spellingShingle | Pasechnik, DV Splitting fields of real irreducible representations of finite groups |
| title | Splitting fields of real irreducible representations of finite groups |
| title_full | Splitting fields of real irreducible representations of finite groups |
| title_fullStr | Splitting fields of real irreducible representations of finite groups |
| title_full_unstemmed | Splitting fields of real irreducible representations of finite groups |
| title_short | Splitting fields of real irreducible representations of finite groups |
| title_sort | splitting fields of real irreducible representations of finite groups |
| work_keys_str_mv | AT pasechnikdv splittingfieldsofrealirreduciblerepresentationsoffinitegroups |