Work

On Formal Degrees of Unipotent Representations

Year: 2021

Type: article

Abstract: Let G be a reductive p-adic group which splits over an unramified extension of the ground field. Hiraga, Ichino and Ikeda [24] 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.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748021000062

Authors: Yongqi Feng, Eric Opdam, Maarten Solleveld

Institutions: Shantou University, University of Amsterdam, Radboud University Nijmegen

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Universiteit van Amsterdam, Radboud Universiteit, Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Award: A Hecke algebra approach to the local Langlands correspondence