Related papers: Epsilon dichotomy for twisted linear models

We give a new proof of the epsilon dichotomy conjecture, stated by Prasad and Takloo-Bighash, for non Archimedean local fields of characteristic zero, when the twisting character is trivial. Our method relies on the functional equation and…

Let $F$ be a non-Archimedean local field. Let $\mathcal{A}_n(F)$ be the set of equivalence classes of irreducible admissible representations of $\textrm{GL}_n(F)$, and $\mathcal{G}_n(F)$ be the set of equivalence classes of n-dimensional…

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 $G=\mathrm{GL}_{2n}(\mathbb{R})$ or $G=\mathrm{GL}_n(\mathbb{H})$ and $H=\mathrm{GL}_n(\mathbb{C})$ regarded as a subgroup of $G$. Here, $\mathbb{H}$ is the quaternion division algebra over $\mathbb{R}$. For a character $\chi$ on…

In this paper we prove a local converse theorem for GL_n over the archimedean local fields, which characterizes an infinitesimal equivalence class of irreducible admissible representations of GL_n(R) (or GL_n(C)) in terms of twisted…

The comprehension of the intricate structure associated to the local symmetries encoded in the tetrad field, as well as its physical meaning, is perhaps the most important unsolved problem within $f(T)$ gravity. This is inextricably…

We prove a local converse theorem for $GL_n$ over the archimedean local fields which characterizes an infinitesimal equivalence class of irreducible admissible representations of $GL_n(\mathbb{R})$ or $GL_n(\mathbb{C})$ in terms of twisted…

A well-known combinatorial algorithm can decide generic rigidity in the plane by determining if the graph is of Pollaczek-Geiringer-Laman type. Methods from matroid theory have been used to prove other interesting results, again under the…

Let F be a p-adic field and n a positive integer. The local Langlands conjecture asserts the existence of a bijection between irreducible admissible representations of GL(n,F) and n-dimensional admissible representations of the Weil-Deligne…

In this paper, we obtain geometric expansions of a local trace formula and its twisted variant for the twisted Gan-Gross-Prasad conjecture. As an application, we prove the local twisted Gan-Gross-Prasad conjecture for $U(V_K)/U(V)$ for…

Following a scheme suggested by B. Feigon, we investigate a local relative trace formula in the situation of a reductive $p$ -adic group $G$ relative to a symmetric subgroup $H= \underline{H}(F)$ where $\underline{H}$ is split over the…

By work of John Tate we can associate an epsilon factor with every multiplicative character of a local field. In this paper we determine the explicit signs of the epsilon factors for symplectic type characters of $K^\times$, where $K/F$ is…

For $E/F$ quadratic extension of local fields and $G$ a reductive algebraic group over $F$, the paper formulates a conjecture classifying irreducible admissible representations of $G(E)$ which carry a $G(F)$ invariant linear form, and the…

In this paper, following the method developed by J.-L. Waldspurger and R. Beuzart-Plessis for Bessel models, we study two local relative trace formulas for the local twisted Gan-Gross-Prasad conjecture. By obtaining spectral expansions and…

In this paper, we completely prove a standard conjecture on the local converse theorem for generic representations of GLn(F), where F is a non-archimedean local field.

We consider a class of linear eigenvalue problems depending on a small parameter epsilon in which the series expansion for the eigenvalue in powers of epsilon is divergent. We develop a new technique to determine the precise nature of this…

Following the work of Jean-Loup Waldspurger, we prove the epsilon dichotomy part of the local Gross-Prasad conjecture over $\mathbb{R}$ for tempered local $L$-parameters.

Let $D$ be a quaternion division algebra over a non-archimedean local field $F$ of characteristic zero. Let $E/F$ be a quadratic extension and $\rm{SL}_{n}^{*}(E) = {\rm{GL}}_{n}(E) \cap \rm{SL}_{n}(D)$. We study distinguished…

Let $K$ be a non-archimedean local field and let $G = \mathrm{GL}_n(K)$. We have shown in previous work that the smooth dual $\mathbf{Irr}(G)$ admits a complex structure: in this article we show how the epsilon factors interface with this…

Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\mathrm{GL}_2$ along…