Distance in the Affine Buildings of SL_n and Sp_n
| dc.creator | Setyadi, A. | |
| dc.date | 2005-11-22 | |
| dc.date | 2008-10-19 | |
| dc.date.accessioned | 2026-07-07T12:05:11Z | |
| dc.date.available | 2026-07-07T12:05:11Z | |
| dc.description | For a local field $K$ and $n \geq 2$, let $Ξ_n$ and $Δ_n$ denote the affine buildings naturally associated to the special linear and symplectic groups $\SL_n(K)$ and $\Sp_n(K)$, respectively. We relate the number of vertices in $Ξ_n$ ($n \geq 3$) close (i.e., gallery distance 1) to a given vertex in $Ξ_n$ to the number of chambers in $Ξ_n$ containing the given vertex, proving a conjecture of Schwartz and Shemanske. We then consider the special vertices in $Δ_n$ ($n \geq 2$) close to a given special vertex in $Δ_n$ (all the vertices in $Ξ_n$ are special) and establish analogues of our results for $Δ_n$. | |
| dc.description | 16 pages, 3 figures; minor corrections; accepted for publication in INTEGERS: The Electronic Journal of Combinatorial Number Theory | |
| dc.identifier | https://arxiv.org/abs/math/0511556 | |
| dc.identifier | http://arxiv.org/abs/math/0511556 | |
| dc.identifier | INTEGERS: Electronic Journal of Combinatorial Number Theory 8 (2008), #A48 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208312 | |
| dc.subject | Number Theory | |
| dc.subject | 20E42, 51E24 | |
| dc.title | Distance in the Affine Buildings of SL_n and Sp_n | |
| dc.type | text |