Equivalence of categories between coefficient systems and systems of\n idempotents

2019/12/13 by Thomas Lanard, Lanard, Thomas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1912.06566

openalex publication_date 2019/12/13 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

The consistent systems of idempotents of Meyer and Solleveld allow to\nconstruct Serre subcategories of Rep_R(G), the category of smooth\nrepresentations of a p-adic group G with coefficients in R. In\nparticular, they were used to construct level 0 decompositions when\nR=\\ℤ_\ℓ, \ℓ \≠ p, by Dat for GL_n and the\nauthor for a more general group. Wang proved in the case of GL_n that the\nsubcategory associated with a system of idempotents is equivalent to a category\nof coefficient systems on the Bruhat-Tits building. This result was used by Dat\nto prove an equivalence between an arbitrary level zero block of GL_n and a\nunipotent block of another group. In this paper, we generalize Wang's\nequivalence of category to a connected reductive group on a non-archimedean\nlocal field.\n

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