Related papers: Local metaplectic correspondence and applications

We realize all irreducible unitary representations of the group $\mathrm{SO}_0(n+1,1)$ on explicit Hilbert spaces of vector-valued $L^2$-functions on $\mathbb{R}^n\setminus\{0\}$. The key ingredient in our construction is an explicit…

Let $G$ be a symplectic group over a nonarchimedean local field of characteristic zero and odd residual characteristic. Given an irreducible cuspidal representation of G, we determine its Langlands parameter (equivalently, its Jordan blocks…

The symmetries provided by representations of the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$ are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory…

Let $F$ be a non-archimedean local field of residual characteristic $p$, $\ell\neq p$ be a prime number, and $\mathrm{W}_F$ the Weil group of $F$. We classify the indecomposable $\mathrm{W}_F$-semisimple Deligne…

Over a p-adic field of odd residual characteristic, Gan and Savin proved a correspondence between the Bernstein components of the even and odd Weil representations of the metaplectic group and the components of the trivial representation of…

We investigate recursive properties of certain p-adic Whittaker functions (of which representation densities of quadratic forms are special values). The proven relations can be used to compute them explicitly in arbitrary dimensions,…

Let F be a non-archimedean local field of odd residual characteristic. Let W be a symplectic vector space over F. It is known that there are different Weil representations of a Meteplectic covering group Mp(W). By some twisted actions, we…

Let F be a non-Archimedean local field of residue characteristic p. In this paper, we first compute the reduction modulo p of irreducible smooth representations of a quaternion division algebra over F and of two-dimensional irreducible…

In [HJLLZ24], we proposed a new conjecture on the structure of the unitary dual of connected reductive groups over non-Archimedean local fields of characteristic zero based on their Arthur representations and verified it for all the known…

We study the algebraic framework in which one can define, in the manner of the theta correspondence, a correspondence between representations of two locally profinite groups $H_1$, $H_2$. In particular, we examine when and how such a…

Let $\theta$ and $\theta'$ be a pair of exceptional representations in the sense of Kazhdan and Patterson [KP], of a metaplectic double cover of $GL_n$. The tensor $\theta\otimes\theta'$ is a (very large) representation of $GL_n$. We…

We obtain necessary and sufficient conditions for the admissible vectors of a new unitary non irreducible representation $U$. The group $G$ is an arbitrary semidirect product whose normal factor $A$ is abelian and whose homogeneous factor…

The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant…

Irreducibility results for parabolic induction of representations of the general linear group over a local non-archimedean field can be formulated in terms of Kazhdan--Lusztig polynomials of type $A$. Spurred by these results and some…

This paper develops various foundational results in the locally analytic representation theory of p-adic groups. In particular, we define the functor ``pass to locally analytic vectors'', which attaches to any continuous representation of a…

Let E/F be a quadratic extension of p-adic fields. The local Langlands correspondence establishes a bijection between n-dimensional Frobenius semisimple representations of the Weil-Deligne group of E and smooth, irreducible representations…

Let F be a p-adic field and let G(n) and G`(n) be the metaplectic double covers of the general symplectic group and symplectic group attached to a 2n dimensional symplectic space over F. We show here that if n is odd then all the genuine…

The Weil representation is a particularly significant linear representation of the metaplectic group, used in the study of theta correspondence. In this paper, I introduce a derived category version of the Weil representation in the local…

We classify the irreducible, admissible, smooth, genuine mod p representations of the metaplectic double cover of SL(2,F), where F is a p-adic field and p is odd. We show, using a generalized Satake transform, that each such representation…

We study finite dimensional representations over some Noetherian algebras over a field of characteristic zero. More precisely, we give necessary and sufficient conditions for the category of locally finite dimensional representations to be…