arXiv Open Access 2026

On the depth of the adjoint representations

Arindam Jana Amiya Mondal

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Abstrak

Let $F$ be a non-archimedean local field of odd residual characteristic $p$. The depth of a smooth representation of ${\rm GL}_n(F)$ is an invariant of Local Langlands Correspondence (LLC). The analogous notion on the Galois side of LLC is known as the slope of a local Galois representation. The slope is well related to the Swan conductor for irreducible Galois representations, whereas its behavior is subtle for reducible Galois representations. In this article, we provide an explicit formula for the slope of the adjoint of a Carayol representation of the local Galois group.

Topik & Kata Kunci

math.RT

Penulis (2)

Arindam Jana

Amiya Mondal

Format Sitasi

APA MLA BibTeX

Jana, A., Mondal, A. (2026). On the depth of the adjoint representations. https://arxiv.org/abs/2603.16355

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Informasi Jurnal

Tahun Terbit: 2026
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓