arXiv Open Access 2025

Distinction of the Steinberg representation and the dual group of a symmetric space

Guy Shtotland

Lihat Sumber

Abstrak

We study the distinction of the Steinberg representation of a split reductive group $G$ with respect to a split symmetric subgroup $H \subset G$. We relate this distinction problem to a problem about the existence of a non-zero harmonic function on a certain hyper-graph related to $X = G/H$. We verify the relative local Langlands conjecture for the Steinberg representation by showing that over a $p$-adic field the Steinberg representation is $H$-distinguished if and only if its Langlands parameter factors through the dual group of $X$.

Topik & Kata Kunci

math.RT

Penulis (1)

Guy Shtotland

Format Sitasi

APA MLA BibTeX

Shtotland, G. (2025). Distinction of the Steinberg representation and the dual group of a symmetric space. https://arxiv.org/abs/2501.01701

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓