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Symplectic extension graphs and Ribet's lemma — arXiv:2610.19434

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.19434
License (as archived): CC0-1.0
Archived: 2026-10-15T21:52:55.557Z
SHA-256 of the archived text: 34e5569b2e6c5bd7d2cf87ecd33843930507479a18edab06ab6a6b4c356bdc0d
Stable URL of this page: https://metraipolis.com/documento/dc_2f374c2fd036

How to cite

Symplectic extension graphs and Ribet's lemma — arXiv:2610.19434 — arXiv (en), https://arxiv.org/abs/2610.19434 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2f374c2fd036 (Metraipolis archive dc_2f374c2fd036, sha256 34e5569b2e6c5bd7d2cf87ecd33843930507479a18edab06ab6a6b4c356bdc0d)

BibTeX

@misc{dc2f374c2fd036,
  title = {Symplectic extension graphs and Ribet's lemma — arXiv:2610.19434},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.19434},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2f374c2fd036; sha256 34e5569b2e6c5bd7d2cf87ecd33843930507479a18edab06ab6a6b4c356bdc0d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.19434. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $p$ be an odd prime, and let $\rho\colon G\to \GSp_{2n}(\Z_p)$ be an irreducible symplectic residually multiplicity free representation. We define the symplectic extension graph $\Gamma_\rho^\GSp$ associated with $\rho$ to be the directed graph whose vertices are the residual factors of $\rho$ and a directed edge between two vertices corresponds to a nonsplit extension between the vertices realized by $\rho$. Using the Euclidean Bruhat--Tits building associated with $\GSp_{2n}(\Q_p)$, under some assumptions, we prove the existence of certain paths in $\Gamma_\rho^\GSp$ and show that $\Gamma_\rho^\GSp$ is a disjoint union of nonempty strongly connected subgraphs. Moreover, we provide examples to show that the result we obtain is optimal.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Representation Theory (math.RT) ; Combinatorics (math.CO); Number Theory (math.NT).
Pagina del lavoro: https://arxiv.org/abs/2610.19434 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T21:37:14.451Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).