Arthur R-groups, classical R-groups, and Aubert involutions for SO(2n + 1)

[摘要] For the special orthogonal group G = SO(2n + 1) over a p-adic field, we consider a discrete series representation of a standard Levi subgroup of G. We prove that the Arthur R-group and the classical R-group of $pi$ are isomorphic. If $pi$ is generic, we consider the Aubert involution $hat{pi}$. Under the assumption that $hat{pi}$ is unitary, we prove that the Arthur R-group of $hat{pi}$ is isomorphic to the R-group of $hat{pi}$ defined by Ban (Ann. Sci. École Norm. Sup. 35 (2002), 673–693; J. Algebra 271 (2004), 749–767). This is done by establishing the connection between the A-parameters of $pi$ and $hat{pi}$. We prove that the A-parameter of $hat{pi}$ is obtained from the A-parameter of $pi$ by interchanging the two $extit{SL}(2,mathbb{C})$ components.

[学科分类] 数学（综合）