Related papers: Local Theta correspondence of Tempered Representat…

In this article, we consider the links between parabolic induction and the local Langlands correspondence. We enunciate a conjecture about the (enhanced) Langlands parameters of supercuspidal representation of split reductives $p$-adics…

We prove that Kaletha's local Langlands correspondence for regular supercuspidal representations gives the classical local Jacquet--Langlands correspondence due to Deligne--Kazhdan--Vigneras and Badulescu. As in a former joint paper with…

Orthosympletic Hamiltonians derived from representations of the Temperley-Lieb algebra are presented and solved via the coordinate Bethe Ansatz. The spectra of these Hamiltonians are obtained using open and closed boundary conditions.

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…

Let $F$ be a non-Archimedean locally compact field. Let $\sigma$ and $\tau$ be finite-dimensional semisimple representations of the Weil-Deligne group of $F$. We give strong upper and lower bounds for the Artin and Swan exponents of…

We show that local-global compatibility (at split primes) away from $p$ holds at all points of the $p$-adic eigenvariety of a definite $n$-variable unitary group. The novelty is we allow non-classical points, possibly non-\'{e}tale over…

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…

We give a purely local proof of the explicit Local Langlands Correspondence for $\mathrm{GSp}_4$ and $\mathrm{Sp}_4$. Moreover, we give a unique characterization in terms of stability of $L$-packets and other properties. Finally, in the…

We show that if an irreducible admissible representation of $\mathrm{SO}_{4n}(F)$ has a generalized Shalika model, then its small theta lift to $\mathrm{Sp}_{4n}(F)$ has the symplectic linear model, thus answering a question posed by D.…

Smooth irreducible representations of tori over local fields have been parameterized by Langlands, using class field theory and Galois cohomology. This paper extends this parameterization to central extensions of such tori, which arise…

We present an explicit and computationally actionable blueprint for constructing vector-valued Siegel modular forms associated to real multiplication (RM) abelian surfaces, leveraging the theta correspondence for the unitary dual pair…

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and…

Let (G,H) be one of the equal rank reductive dual pairs (Mp_{2n},O_{2n+1}) or (U_n,U_n) over a non-archimedean local field of characteristic zero. It is well-known that the theta correspondence establishes a bijection between certain…

In this report, we discuss the Seiberg-Witten maps up to the second order in the noncommutative parameter $\theta$. They add to the recently published solutions in [1]. Expressions for the vector, fermion and Higgs fields are given…

For a reductive group over a nonarchimedean local field, we define the stack of spherical Langlands parameters, using the inertia-invariants of the Langlands dual group. This generalizes the stack of unramified Langlands parameters in case…

In this article, we study local zeta functions over non-Archimedean locals fields of arbitrary characteristic attached to rational functions and characters $\chi$ of the units of the ring of integers $\mathcal{O}_{K}$, by using an approach…

In this paper, we prove that theta correspondence preserves unitarity under certain restrictions.

The local reggeon field theory is studied perturbatively taking advantage of the PT symmetry in the Hamiltonian formulation. In the lowest non trivial order we show that the pomeron interactions renormalize the slope. In the same order we…

We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of mock theta functions. By comparing the different…

We combine the Duke-Imamoglu-Ikeda lifting with the theta lifting to produce new CAP representations of metaplectic, symplectic and orthogonal groups. These constructions partially generalize the theories of Waldspurger on the Shimura…