On depth-zero characters of p-adic groups

2025/02/03 by Maarten Solleveld, Yujie Xu, Solleveld, Maarten +1 · 2 citations
Mathematics · #advanced mathematical theories #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory

paper · pdf · doi:10.4310/mrl.260614172949

Abstract

We show new properties of the Langlands correspondence for arbitrary tori over local fields. Furthermore, we give a detailed analysis of depth-zero characters of reductive p-adic groups, for groups that may be wildly ramified. We present several different definitions of “depth-zero” for characters, and show that these notions are in fact equivalent. These results are useful for proving new cases of local Langlands correspondences, in particular for depth-zero representations.

Citations

• Hecke algebras and local Langlands correspondence for non-singular depth-zero representations

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• Formal degree of principal series of quasi-split groups
• Langlands parameters for Moy-Prasad types

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