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

2025/01/03 by Guy Shtotland, Shtotland, Guy
Mathematics · Medicine · #22E50 #Advanced Algebra and Geometry #Advanced Neuroimaging Techniques and Applications #Advanced Operator Algebra Research #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2501.01701

openalex publication_date 2025/01/03 · openalex created_date 2025/01/07 · openalex updated_date 2026/07/28

Abstract

We study the distinction of the Steinberg representation of a split reductive group G with respect to a split symmetric subgroup H ⊂ 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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