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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.07198
- arXiv:
- arXiv:1910.07198
- Bibcode:
- 2019arXiv191007198F
- Keywords:
-
- Mathematics - Representation Theory;
- 22E50 (11S37;
- 20G25)
- E-Print:
- J. Inst. Math. Jussieu (2021)