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arXiv · 2501.01701

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

Guy Shtotland
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Abstract

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 $X$.

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Guy Shtotland. 2025-01-03. Distinction of the Steinberg representation and the dual group of a symmetric space. https://arxiv.org/abs/2501.01701

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