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. G connected reductive group defined over E let M:=RE/FG the F obtained by Weil restriction scalars. We investigate depth, enhanced Langlands correspondence, in transition from G(E) to M(F). obtain depth-comparison formula for Weil-restricted groups.