Journal of the Institute of Mathematics of Jussieu ( IF 0.9 ) Pub Date : 2021-03-19 , DOI: 10.1017/s1474748021000062 Yongqi Feng , Eric Opdam , Maarten Solleveld
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.
中文翻译:
关于单能表示的形式度
设G是一个还原的p进群,它在基场的一个未分支的扩展上分裂。Hiraga、Ichino 和 Ikeda [24] 推测,平方可积G表示 $\pi$ 的形式度可以用 $\ pi $的增强 L 参数的 伴随 $\gamma$ 因子来表示. 对回火不可约G表示的 Plancherel 密度提出了类似的猜想。
我们证明了单能G表示的这些猜想。我们还为所涉及的伴随 $\gamma $ 因子导出了显式公式。