Smooth representations of unit groups of split basic algebras over\n non-Archimedean local fields

2019/10/31 by Carlos A. M. André, André, Carlos A. M., João Dias +1
Mathematics · #20G25(Primary) 22D12 #22D30 (Secondary) #Advanced Algebra and Geometry #FOS: Mathematics #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1910.14639

openalex publication_date 2019/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider smooth representations of the unit group G =\n\A^\× of a finite-dimensional split basic algebra \A\nover a non-Archimedean local field. In particular, we prove a version of\nGutkin's conjecture, namely, we prove that every irreducible smooth\nrepresentation of G is compactly induced by a one-dimensional representation\nof the unit group of some subalgebra of \A. We also discuss\nadmissibility and unitarisability of smooth representations of G.\n

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