Kazhdan constants for Chevalley groups over the integers
We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than A<sub>n</sub>, these are the first explicit asymptotically sharp such bounds. The method relies on establishing a new connection betwe...
| Autores principales: | , |
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| Formato: | Journal article |
| Lenguaje: | English |
| Publicado: |
EMS Press
2024
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| _version_ | 1826316088626905088 |
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| author | Kaluba, M Kielak, D |
| author_facet | Kaluba, M Kielak, D |
| author_sort | Kaluba, M |
| collection | OXFORD |
| description | We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than A<sub>n</sub>, these are the first explicit asymptotically sharp such bounds. The method relies on establishing a new connection between the structure of a root system grading a family of groups and the behaviour of the square of the Laplace operator in the family. |
| first_indexed | 2024-12-09T03:37:34Z |
| format | Journal article |
| id | oxford-uuid:9de09c14-1913-4122-aa47-2a016780e698 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:37:34Z |
| publishDate | 2024 |
| publisher | EMS Press |
| record_format | dspace |
| spelling | oxford-uuid:9de09c14-1913-4122-aa47-2a016780e6982024-12-02T09:33:44ZKazhdan constants for Chevalley groups over the integersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9de09c14-1913-4122-aa47-2a016780e698EnglishSymplectic ElementsEMS Press2024Kaluba, MKielak, DWe compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than A<sub>n</sub>, these are the first explicit asymptotically sharp such bounds. The method relies on establishing a new connection between the structure of a root system grading a family of groups and the behaviour of the square of the Laplace operator in the family. |
| spellingShingle | Kaluba, M Kielak, D Kazhdan constants for Chevalley groups over the integers |
| title | Kazhdan constants for Chevalley groups over the integers |
| title_full | Kazhdan constants for Chevalley groups over the integers |
| title_fullStr | Kazhdan constants for Chevalley groups over the integers |
| title_full_unstemmed | Kazhdan constants for Chevalley groups over the integers |
| title_short | Kazhdan constants for Chevalley groups over the integers |
| title_sort | kazhdan constants for chevalley groups over the integers |
| work_keys_str_mv | AT kalubam kazhdanconstantsforchevalleygroupsovertheintegers AT kielakd kazhdanconstantsforchevalleygroupsovertheintegers |