Related papers: Local Theta Correspondences between Supercuspidal …

We show that some types for supercuspidal representations of tamely ramified $p$-adic groups that appear in Jiu-Kang Yu's work are geometrizable. To do so, we define a function-sheaf dictionary for one-dimensional characters of arbitrary…

For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced…

We compare precisely and explicitly Bushnell-Kutzko and Yu's constructions of supercuspidal representations. At the end, we draw conclusions and ask a natural question about the existence of a general construction.

We classify what we call ``typically almost symmetric'' depth zero supercuspidal representations of classical groups into L-packets. Our main results resolve an ambiguity in the paper of Lust-Stevens \cite{Lust-Stevens} in this case, where…

We construct a class of $\ell$-adic local systems on $\mathbb{A}^1$ that generalizes the Airy sheaves defined by N. Katz to reductive groups. These sheaves are finite field analogues of generalizations of the classical Airy equation…

This set of lecture notes on local theta correspondence is the written version of a mini-course the author gave in March of 2025 for the program ``Representation Theory and Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris.…

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation $\pi$ of a connected reductive $p$-adic group, subject to the assumption that $\pi$ is obtained via induction from a representation of…

In this work, we explicitly compute a certain family of twisted gamma factors of a simple supercuspidal representation $\pi$ of a $p$-adic odd orthogonal group. These computations, together with analogous computations for general linear…

We introduce a revised notion of depth for Langlands parameters for tori defined over a nonarchimedean local field \(F\) that restores depth preservation under the local Langlands correspondence (LLC). We leverage that preservation to…

In his article "Transcending Classical Invariant Theory" (J.A.M.S., 1989, Vol 2), Roger Howe established a correspondence between representations of a dual pair of reductive groups. This correspondence is known as Howe's correspondence or…

By using results on poles of $L$-functions and theta correspondence, we give a bound on $b$ for $(\chi,b)$-factors of the global Arthur parameter of a cuspidal automorphic representation $\pi$ of a classical group or a metaplectic group…

Let $F$ be a $p$-adic field of characteristic 0, and let $M$ be an $F$-Levi subgroup of a connected reductive $F$-split group such that $\Pi_{i=1}^{r} SL_{n_i} \subseteq M \subseteq \Pi_{i=1}^{r} GL_{n_i}$ for positive integers $r$ and…

We develop a general strategy for constructing the explicit Local Langlands Correspondences for $p$-adic reductive groups via reduction to LLC for supercuspidal representations of proper Levi subgroups, using Hecke algebra techniques. As an…

Let $(\mathbb{G},\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\neq 2$, attached to the involution $\theta$. Under the assumption that there exists a maximally $\theta$-split torus in $\mathbb{G}$, which…

Let $F$ be a non-archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. To construct types for supercuspidal representations of $G$, simple types by S\'echerre--Stevens and Yu's…

Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations $\sigma$ of unitary groups and investigate their relation with the occurrence of a simple global…

Using theta correspondence, we obtain a classification of irreducible representations of an arbitrary even orthogonal group (i.e. the local Langlands correspondence) by deducing it from the local Langlands correspondence for symplectic…

For a connected reductive group $G$ over a non-archime\-dean local field $F$ of positive characteristic, Genestier and Lafforgue have attached a semisimple parameter $\CL^{ss}(\pi)$ to each irreducible representation $\pi$. Our first result…

We study the functoriality of the local theta correspondence for classical $p$-adic groups. This is realized via the adaptation of the Adams conjecture to ABV-packets. We provide evidence for the conjecture, especially in the case of…

We establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes. For the tame supercuspidals constructed by J.-K. Yu we prove the limit multiplicity…