Spectral correspondences for affine Hecke algebras

2013/10/27 by Opdam, Eric · 2 citations
#43A30 #FOS: Mathematics #Primary 20C08 #Representation Theory (math.RT) #Secondary 22D25

paper · doi:10.48550/arxiv.1310.7193

Abstract

We introduce the notion of spectral transfer morphisms between normalized affine Hecke algebras, and show that such morphisms induce spectral measure preserving correspondences on the level of the tempered spectra of the affine Hecke algebras involved. We define a partial ordering on the set of isomorphism classes of normalized affine Hecke algebras, which plays an important role for the Langlands parameters of Lusztig's unipotent representations.

Cited by

• Formal degree of principal series of quasi-split groups
• The Hiraga-Ichino-Ikeda Conjecture for Principal Series of Split p-adic Groups

Related

• Spectral transfer morphisms for unipotent affine Hecke algebras
• Affine Hecke algebras for Langlands parameters
• Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda
• Correspondences between affine Hecke algebras and applications
• The Spectral Hecke Algebra