Depth-preserving property of the local Langlands correspondence for quasi-split classical groups in large residual characteristic

For a quasi-split classical group over p-adic field with sufficiently large residual characteristic, we prove that the maximum depth of representation in each L-packet equals corresponding L-parameter. Furthermore, for unitary groups, show is constant L-packet. The key an analysis endoscopic character relation via harmonic based on Bruhat–Tits theory. These results are slight generalizations result Ganapathy and Varma.