Depth and the local Langlands correspondence

Abstract

Let G be an inner form of a general linear group over a non-archimedean local field. We prove that the local Langlands correspondence for G preserves depths. We also show that the local Langlands correspondence for inner forms of special linear groups preserves the depths of essentially tame Langlands parameters.

The proof of Lemma 3.2 in the first version contained a mistake. In the second version the analysis of depth for inner forms of SL_n was extended and paragraph 2.4 was simplified

References in corpus (3)

• Geometric structure and the local Langlands conjecture
• Preservation of depth in local geometric Langlands correspondence
• Stabilite en niveau 0 pour les groupes orthogonaux impairs p-adiques

Cited by in corpus (3)

• Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations I: tame case
• A constraint for twist equivalence of cusp forms on GL$(n)$
• L-packets and depth for SL_2(K) with K a local function field of characteristic 2