Related papers: Local Jacquet-Langlands correspondence for regular…
In this paper, we prove that theta correspondence preserves unitarity under certain restrictions.
Using a level-raising argument (and a result of Larsen on the image of Galois representations in compatible systems), we prove that for any automorphic representation $\pi$ for $\U(3)$, the $l$-adic Galois representation $\rho_l$ which is…
We construct a family of affinoids in the Lubin-Tate perfectoid space and their formal models such that the middle cohomology of their reductions realizes the local Langlands correspondence and the local Jacquet-Langlands correspondence for…
Persistence of non-degeneracy is a phenomenon which appears in the theory of $\overline{\mathbb Q}_l$-representations of the linear group: every irreducible submodule of the restriction to the mirabolic sub-representation of a…
For a reductive group $G$ over a local non-archimedean field $K$ one can mimic the construction from the classical Deligne--Lusztig theory by using the loop space functor. We study this construction in special the case that $G$ is an inner…
The goal of this paper is to give a simple proof of Deligne's conjecture (proven by Fujiwara) and to generalize it to the situation appearing in our joint project with David Kazhdan on the global Langlands correspondence over function…
In this paper, we completely describe the Howe correspondence for the dual pairs from the title over a nonarchimedean local field of characteristic zero. More specifically, for every irreducible admissible representation of these groups, we…
The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of $G_2$ over a $p$-adic field, one can associate a generic supercuspidal irreducible representation of either $PGSp_6$ or$PGL_3$. We prove…
Refined forms of the local Langlands correspondence seek to relate representations of reductive groups over local fields with sheaves on stacks of Langlands parameters. But what kind of sheaves? Conjectures in the spirit of Kazhdan-Lusztig…
We discuss a general framework for the analytic Langlands correspondence over an arbitrary local field F introduced and studied in our works arXiv:1908.09677, arXiv:2103.01509 and arXiv:2106.05243, in particular including non-split and…
In this paper we prove some orthogonality relations for representations arising from deep level Deligne--Lusztig schemes of Coxeter type. This generalizes previous results of Lusztig (2004), and of Chan and the second author (2019).…
We prove the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case under some assumptions. This is the last case of the local Gan-Gross-Prasad conjectures. We also prove two of Prasad's conjectures on the local theta…
This paper studies the behavior of Jiu-Kang Yu's tame supercuspidal representations relative to involutions of reductive p-adic groups. Symmetric space methods are used to illuminate various aspects of Yu's construction. Necessary…
The author's work with Murnaghan on distinguished tame supercuspidal representations is re-examined using a simplified treatment of Jiu-Kang Yu's construction of tame supercuspidal representations of $p$-adic reductive groups. This leads to…
A paper of Reeder-Yu gives a construction of epipelagic supercuspidal representations of $p$-adic groups. The input for this construction is a pair $(\lambda, \chi)$ where $\lambda$ is a stable vector in a certain representation coming from…
We use the patching method of Taylor--Wiles and Kisin to construct a candidate for the p-adic local Langlands correspondence for GL_n(F), F a finite extension of Q_p. We use our construction to prove many new cases of the Breuil--Schneider…
We prove the local Gross-Prasad conjecture for generic L-packets of representations of special orthogonal groups. The proof uses the same result for tempered L-packets proved in a preceding paper, and irreducibility results for the induced…
We prove that certain Galois-isotypic parts of the completed cohomology group for U(2) can be written as a completed tensor product of a representation coming from the p-adic Langlands correspondence for $GL_2(\mathbb{Q}_p)$ and a…
We prove that the conjectural depth zero local Langlands correspondence of DeBacker/Reeder agrees with the depth zero local Langlands correspondence as described by Moy, for the group $GL(\ell,F)$, where $\ell$ is prime and F is a local…
In this paper, we give a new realization of the local Langlands correspondence for PGL(2,F), where F is a p-adic field of odd residual characteristic. In this case, supercuspidal representations of PGL(2,F) are parameterized by characters…