On compatibility in restriction of Arthur’s conjecture for R-groups

We investigate the compatibility of Arthur’s conjecture for R-groups in the restriction of discrete series representations from Levi subgroups of a p-adic group to those of its closed subgroup having the same derived group. The relation is conditional as it holds under the conjectural local Langlands correspondence in general. This work provides a uniform way to verify Arthur’s conjecture for R-groups in the setting. It can be also applied to several cases where those assumptions are already established.