相关论文: Characterization of \gamma-factors: the Asai case

Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and…

We prove explicit rationality-results for Asai- $L$-functions, $L^S(s,\Pi',{\rm As}^\pm)$, and Rankin-Selberg $L$-functions, $L^S(s,\Pi\times\Pi')$, over arbitrary CM-fields $F$, relating critical values to explicit powers of $(2\pi i)$.…

In the first part of this series of papers we propose a functional integral representation for local Archimedean L-factors given by products of the Gamma-functions. In particular we derive a representation of the Gamma-function as a…

Let $N$ be a simply connected, connected nilpotent Lie group which admits a uniform subgroup $\Gamma.$ Let $\alpha$ be an automorphism of $N$ defined by $\alpha\left( \exp X\right) =\exp AX.$ We assume that the linear action of $A$ is…

We compute the local twisted exterior square gamma factors for simple supercuspidal representations, using which we prove a local converse theorem for simple supercuspidal representations.

We study two global structural properties of a graph $\Gamma$, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erd\"os--R\'enyi random graph model G(n,p), proving a sharp…

Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\ell$ a prime number, $\ell \neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensional, smooth representations of the Weil group of…

Consider a Riemannian symmetric space $X= G/K$ of non-compact type, where $G$ denotes a connected, real, semi-simple Lie group with finite center, and $K$ a maximal compact subgroup of $G$. Let $\widetilde X$ be its Oshima compactification,…

We construct a theory of local gamma factors for $G_2 \times GL_r$ using a functorial lifting from $G_2$ to $GL_7$. This theory of gamma factors is uniquely characterized by a usual list of properties, showing that it is the only possible…

We construct stable geometric and spectral transfer factors for a general reductive group and develop some of their basic properties, assuming the refined local Langlands correspondence. Using our definition of stable geometric transfer…

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…

Let $F$ be a non-archimedean local field, of characteristic 0. Let $V$ be a finite dimensional vector space over $F$ and $q$ be a non-degenerate quadratic form on $V$. Denote $G$ the special orthogonal group of $(V,q)$. Let $W$ a…

After extending the theory of Rankin-Selberg local factors to pairs of $\ell$-modular representations of Whittaker type, of general linear groups over a non-archimedean local field, we study the reduction modulo $\ell$ of $\ell$-adic local…

Let $F$ be a non-Archimedean locally compact field of residual characteristic $p$ with Weil group $\Cal W_F$. Let $\sigma$ be an irreducible smooth complex representation of $\Cal W_F$, realized as the Langlands parameter of an irreducible…

Let $E$ be a non-Archimedian local field of characteristic zero and residue characteristic $p$. Let ${\bf G}$ be a connected reductive group defined over $E$ and $\pi$ an irreducible admissible representation of $G={\bf G}(E)$. A result of…

In this paper we prove some generalizations of the classical Hasse-Davenport product relation for certain arithmetic factors defined on p-adic fields, among them one finds the epsilon-factors appearing in Tate's thesis. We then show that…

Let $F$ be a non--Archimedean locally compact field (${\rm car}(F)\geq 0$), ${\bf G}$ be a connected reductive group defined over $F$, $\theta$ be an $F$--automorphism of ${\bf G}$, and $\omega$ be a character of ${\bf G}(F)$. We fix a Haar…

Irreducible sigma models, i.e. those for which the partition function does not factorise, are defined on Riemannian spaces with irreducible holonomy groups. These special geometries are characterised by the existence of covariantly constant…

We consider an $n$-fold Brylinski-Deligne cover of a reductive group over a $p$-adic field. Since the space of Whittaker functionals of an irreducible genuine representation of such a cover is not one-dimensional, one can consider a local…

Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $\theta$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_\theta(G) \subseteq V$ of semistable points. We give necessary,…