On formal degrees of unipotent representations

Yongqi Feng, Eric Opdam, Maarten Solleveld

Published 2019-10-16Version 1

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.