Comparison of the depths on both sides of the local Langlands correspondence for Weil-restricted groups (with an appendix by Jessica Fintzen)

Let E/F be a finite and Galois extension of non-archimedean local fields. Let G be a connected reductive group defined over E and let M:=RE/FG be the reductive group over F obtained by Weil restriction of scalars. We investigate depth, and the enhanced local Langlands correspondence, in the transition from G(E) to M(F). We obtain a depth-comparison formula for Weil-restricted groups.