2016/11/21 by Xuhua He, He, Xuhua
Mathematics · #20C08 #22E50 #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.1611.06825
openalex publication_date 2016/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study some relation between the cocenter H(G) of the Hecke algebra H(G) of a connected reductive group G over an nonarchimedean local field and the cocenter H(M) of its Levi subgroups M. Given any Newton component of H(G), we construct the induction map i from the corresponding Newton component of H(M) to it. We show that this map is surjective. This leads to the Bernstein-Lusztig type presentation of the cocenter H(G), which generalizes the work \citeHN2 on the affine Hecke algebras. We also show that the map i we constructed is adjoint to the Jacquet functor and in characteristic 0, the map i is an isomorphism.