Geometric structure in smooth dual and local Langl

Authors: AnneMarie Aubert Paul Baum Roger Plymen Maarten Solleveld

Publish Date: 2014/05/23

Volume: 9, Issue: 2, Pages: 99-136

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Abstract

This expository paper first reviews some basic facts about padic fields reductive padic groups and the local Langlands conjecture If G is a reductive padic group then the smooth dual of G is the set of equivalence classes of smooth irreducible representations of G The representations are on vector spaces over the complex numbers In a canonical way the smooth dual is the disjoint union of subsets known as the Bernstein components According to a conjecture due to ABPS Aubert–Baum–Plymen–Solleveld each Bernstein component has a geometric structure given by an appropriate extended quotient The paper states this ABPS conjecture and then indicates evidence for the conjecture and its connection to the local Langlands conjecture

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