Correspondences between affine Hecke algebras and applications

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.

arXiv commentPresentation has been improved, misprints have been corrected

References in corpus (9)

• Local Theta correspondence of Tempered Representations and Langlands parameters
• Affine Hecke algebras for Langlands parameters
• Howe Correspondence of Unipotent Characters for a Finite Symplectic/Even-orthogonal Dual Pair
• Lusztig Correspondence and Howe Correspondence for Finite Reductive Dual Pairs
• The stable Bernstein center and test functions for Shimura varieties
• On Theta and Eta Correspondences for Finite Symplectic/Orthogonal Dual Pairs
• Hecke algebras for $p$-adic reductive groups and Local Langlands Correspondence for Bernstein blocks
• Equal rank local theta correspondence as a strong Morita equivalence
• A stacky generalized Springer correspondence and rigid enhancements of L-parameters