English

On formal degrees of unipotent representations

Representation Theory 2022-10-11 v1

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 π\pi can be expressed in terms of the adjoint γ\gamma-factor of the enhanced L-parameter of π\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 γ\gamma-factors.

Keywords

Cite

@article{arxiv.1910.07198,
  title  = {On formal degrees of unipotent representations},
  author = {Yongqi Feng and Eric Opdam and Maarten Solleveld},
  journal= {arXiv preprint arXiv:1910.07198},
  year   = {2022}
}