Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914474486661120 |
|---|---|
| author | Shen, Jianhao |
| author_facet | Shen, Jianhao |
| contents | For the Tits building B(G) of a finite group of Lie type G(Fq), we study the edge zeta function, which enumerates edge-geodesic cycles in the 1-skeleton. We show that every nonzero edge eigenvalue becomes a power of q after raising to a bounded exponent k depending on the type of G. The proof is uniform across types using a Hecke algebra approach. This extends previous results for type A and for oppositeness graphs to the full edge-geodesic setting and all finite groups of Lie type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type Shen, Jianhao Combinatorics Number Theory Representation Theory For the Tits building B(G) of a finite group of Lie type G(Fq), we study the edge zeta function, which enumerates edge-geodesic cycles in the 1-skeleton. We show that every nonzero edge eigenvalue becomes a power of q after raising to a bounded exponent k depending on the type of G. The proof is uniform across types using a Hecke algebra approach. This extends previous results for type A and for oppositeness graphs to the full edge-geodesic setting and all finite groups of Lie type. |
| title | Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type |
| topic | Combinatorics Number Theory Representation Theory |
| url | https://arxiv.org/abs/2405.14395 |