On growth types of quotients of Coxeter groups by parabolic subgroups
| dc.creator | Viswanath, Sankaran | |
| dc.date | 2006-01-19 | |
| dc.date | 2006-03-01 | |
| dc.date.accessioned | 2026-07-07T06:59:06Z | |
| dc.date.available | 2026-07-07T06:59:06Z | |
| dc.description | The principal objects studied in this note are Coxeter groups $W$ that are neither finite nor affine. A well known result of de la Harpe asserts that such groups have exponential growth. We consider quotients of $W$ by its parabolic subgroups and by a certain class of reflection subgroups. We show that these quotients have exponential growth as well. To achieve this, we use a theorem of Dyer to construct a reflection subgroup of $W$ that is isomorphic to the universal Coxeter group on three generators. The results are all proved under the restriction that the Coxeter diagram of $W$ is simply laced, and some remarks made on how this restriction may be relaxed. | |
| dc.description | 10 pages; The exposition has been made more concise and an additional proposition is proved in the final section | |
| dc.identifier | https://arxiv.org/abs/math/0601482 | |
| dc.identifier | http://arxiv.org/abs/math/0601482 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107623 | |
| dc.subject | Group Theory | |
| dc.subject | 20F55 | |
| dc.title | On growth types of quotients of Coxeter groups by parabolic subgroups | |
| dc.type | text |