Correspondences between affine Hecke algebras and applications

2023/11/06 by Anne‐Marie Aubert, Aubert, Anne-Marie
Mathematics · #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.2311.03203

openalex publication_date 2023/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We review the construction of generalized affine Hecke algebras attached to Bernstein series of both smooth irreducible and enhanced L-parameters of p-adic reductive groups and apply it to the study of the Howe correspondence.

Citations

• Affine Hecke algebras for Langlands parameters
• Howe Correspondence of Unipotent Characters for a Finite Symplectic/Even-orthogonal Dual Pair
• Equal rank local theta correspondence as a strong Morita equivalence
• A stacky generalized Springer correspondence and rigid enhancements of L-parameters
• Hecke algebras for p-adic reductive groups and Local Langlands Correspondences for Bernstein blocks

Related

• Affine Hecke algebras for Langlands parameters
• Affine Hecke algebras for classical p-adic groups
• Hecke algebras for p-adic reductive groups and Local Langlands Correspondences for Bernstein blocks
• Hermitian duals and generic representations for affine Hecke algebras
• A formula of Arthur and affine Hecke algebras