On formal degrees of unipotent representations

Abstract

Let G be a reductive p-adic group which splits over an unramified extension of the ground field. Hiraga, Ichino and Ikeda conjectured that the formal degree of a square-integrable G-representation $\pi$ can be expressed in terms of the adjoint $\gamma$-factor of the enhanced L-parameter of $\pi$. A similar conjecture was posed for the Plancherel densities of tempered irreducible G-representations. We prove these conjectures for unipotent G-representations. We also derive explicit formulas for the involved adjoint $\gamma$-factors.

References in corpus (8)

• Affine Hecke algebras for Langlands parameters
• On a uniqueness property of cuspidal unipotent representations
• On formal degrees of unipotent representations
• A uniform classification of discrete series representations of affine Hecke algebras
• Langlands parameters, functoriality and Hecke algebras
• Rigid inner forms over local function fields
• Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda
• A Note on the Spectral Transfer Morphisms for Affine Hecke Algebras

Cited by in corpus (4)

• On formal degrees of unipotent representations
• The Wavefront Sets of Unipotent Supercuspidal Representations
• On principal series representations of quasi-split reductive p-adic groups
• A nonabelian Fourier transform for tempered unipotent representations