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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 $M: = mathfrak{R}_{E/F}, G$ 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.
Let $K$ be a non-archimedean local field. In the local Langlands correspondence for tori over $K$, we prove an asymptotic result for the depths.
We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified) local model
Let H be any reductive p-adic group. We introduce a notion of cuspidality for enhanced Langlands parameters for H, which conjecturally puts supercuspidal H-representations in bijection with such L-parameters. We also define a cuspidal support map and
In this joint introduction to an Asterisque volume, we give a short discussion of the historical developments in the study of nonlinear covering groups, touching on their structure theory, representation theory and the theory of automorphic forms. Th
A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. In this paper, we describe