Epsilon factors as algebraic characters on the smooth dual of\n \GL_n

2016/06/05 by Roger Plymen, Plymen, Roger
Mathematics · #20G25 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1606.01497

openalex publication_date 2016/06/05 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let K be a non-archimedean local field and let G = \GL_n(K). We\nhave shown in previous work that the smooth dual \Irr(G) admits a\ncomplex structure: in this article we show how the epsilon factors interface\nwith this complex structure. The epsilon factors, up to a constant term, factor\nas invariant characters through the corresponding complex tori. For the\narithmetically unramified smooth dual of \GL_n, we provide explicit\nformulas for the invariant characters.\n

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