The Bernstein center of a p-adic unipotent group
نویسندگان
چکیده
منابع مشابه
ON THE CHARACTERS OF UNIPOTENT REPRESENTATIONS OF A SEMISIMPLE p-ADIC GROUP
Let G be a semisimple almost simple algebraic group defined and split over a nonarchimedean local field K and let V be a unipotent representation of G(K) (for example, an Iwahori-spherical representation). We calculate the character of V at compact very regular elements of G(K).
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0.1. Let K be a nonarchimedean local field with a residue field of cardinal q. Let G(K) be the group of K-rational points of a connected, adjoint simple algebraic group G defined over K which becomes split over an unramified extension of K. Let U(G(K)) be the set of isomorphism classes of unipotent representations of G(K) (see [L4, 1.21]). Let G be a simply connected almost simple algebraic gro...
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Let G(K) be the group of K-rational points of a connected adjoint simple algebraic group over a nonarchimedean local field K. In this paper we classify the unipotent representations of G(K) in terms of the geometry of the Langlands dual group. This was known earlier in the special case where G(K) is an inner form of a split group.
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For a certain class of locally profinite groups, we show that an irreducible smooth discrete series representation is necessarily supercuspidal and, more strongly, can be obtained by induction from a linear character of a suitable open and compact modulo center subgroup. If F is a non-Archimedean local field, then our class of groups includes the groups of F -points of unipotent algebraic group...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2020
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2020.04.035