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

2024/11/29 by Maarten Solleveld, Yujie Xu, Solleveld, Maarten +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Black Holes and Theoretical Physics

paper · pdf · doi:10.1017/fms.2026.10198

Abstract

Abstract Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G -representation is non-singular if its cuspidal support is non-singular. We establish a local Langlands correspondence for all such representations. We obtain it as a specialization from a categorical version: an equivalence between the category of finite-length non-singular depth-zero G -representations and the category of finite-length right modules of a direct sum of twisted affine Hecke algebras constructed from Langlands parameters. We also show that our LLC and our equivalence of categories have several nice properties, for example, compatibility with parabolic induction and with twists by depth-zero characters.

Citations

• Hecke algebras for p-adic reductive groups and Local Langlands Correspondences for Bernstein blocks

Cited by

• A generic categorical local Langlands correspondence for quasi-split reductive groups
• On depth-zero characters of p-adic groups

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