Rationality properties of complex representations of reductive p-adic groups

2025/10/28 by Kazhdan, David, Solleveld, Maarten, Varshavsky, Yakov · 1 citation
#20G25 #22E50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.24201

Abstract

For a reductive group G over a non-archimedean local field, we compare smooth representations over C with smooth representations over Qbar (an algebraic closure of Q). For example, we show that tensoring with C over Qbar preserves irreducibility of representations. We also show that an elliptic G-representation (in the sense of Arthur) can be realized over Qbar if and only if its central character takes values in Qbar. That applies in particular to all essentially square-integrable G-representations. We also study the action of the automorphism group of C/Q on complex G-representations. We prove that the classes of essentially square-integrable representations and of elliptic representations are stable under Aut(C/Q).

Citations

• Standard modules and intertwining operators for reductive p-adic groups
• Endoscopic decomposition of elliptic Fargues-Scholze L-packets
• On the generalized Ramanujan and Arthur conjectures over function fields
• Geometrization of the local Langlands correspondence
• Correspondance de Jacquet-Langlands pour les corps locaux de caractéristique non nulle

Cited by

• Standard modules and intertwining operators for reductive p-adic groups

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