Related papers: Interpolating local constants in families

Pairs $\aa \subset \bb$ of local quantum field theories are studied, where $\aa$ is a chiral conformal \qft and $\bb$ is a local extension, either chiral or two-dimensional. The local correlation functions of fields from $\bb$ have an…

Geometric Langlands predicts an isomorphism between Whittaker coefficients of Eisenstein series and functions on the moduli space of $\check{N}$-local systems. We prove this formula by interpreting Whittaker coefficients of Eisenstein…

This is the second of two papers introducing and investigating two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. In the first part, we proved some of their properties such as…

Behind this sophisticated title hides an elementary exercise on Clifford theory for index two subgroups and self-dual/conjugate-dual representations. When applied to semi-simple representations of the Weil-Deligne group $W'_F$ of a non…

We study a function $\mathcal{L}_{\Gamma}$ which quantifies the LEF (local embeddability into finite groups) property for a finitely generated group $\Gamma$. We compute this "LEF growth" function in some examples, including certain wreath…

We give a general identity relating Eisenstein series on general linear groups. We do it by constructing an Eisenstein series, attached to a maximal parabolic subgroup and a pair of representations, one cuspidal and the other a character,…

Let $G$ be a $p$-adic Lie group with reductive Lie algebra $\mathfrak{g}$. In analogy to the translation functors introduced by Bernstein and Gelfand on categories of $U(\mathfrak{g})$-modules we consider similarly defined functors on the…

In this paper, we partially complete the local Rankin-Selberg theory of Asai $L$-functions and $\epsilon$-factors as introduced by Flicker and Kable. In particular, we establish the relevant local functional equation at Archimedean places…

Grassmannian local hidden variables are shown to generate all possible quantum correlations in a bipartite quantum system. Grassmann representation of fermions, common in field theory, opens a related perspective. Although Grassmann hidden…

Let $G$ be a split connected reductive group over a non-archimedean local field. In the $p$-adic setting, Orlik-Strauch constructed functors from the BGG category $\mathcal{O}$ associated to the Lie algebra of $G$ to the category of locally…

This paper verifies $n\times 1$ Local Converse Theorem for twisted gamma factors of irreducible cuspidal representations of ${\rm GL}_n({\mathbb F}_p)$, for $n\leq 5,$ and of irreducible generic representations, for…

In this paper, we prove the fundamental properties of gamma factors defined by Rankin-Selberg integrals of Shimura type for pairs of generic representations $(\pi, \tau)$ of $\mathrm{U}_{2\ell}(F)$ and $\mathrm{GL}_n(E)$ for a local field…

We prove a result which provides a link between the decomposition of parabolically induced representations and the Bushnell--Kutzko theory of typical representations. As an application, we show that there exists a well-defined inertial…

Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for…

We investigate the behaviour of the reduction type and related invariants of curves in families of curves over a discretely valued field. By a family, we will mean a set of curves obtained by perturbing the coefficients of the defining…

In this paper we characterize irreducible generic representations of $\SO_{2n+1}(k)$ where $k$ is a $p$-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic…

Let $\ell$ be a prime number different from the residue characteristic of a non-archimedean local field $F$. We give formulations of $\ell$-adic local Langlands correspondences for connected reductive algebraic groups over $F$, which we…

In group representations several inductions given by tensoring with appropriate bimodules may be reconstructed via homology of $G$-posets with $G$-equivariant coefficients. For this purpose, we need various local categories of a finite…

By Langlands and Deligne we know that the local constants are extendible functions. Therefore, to give an explicit formula of the local constant of an induced representation of a local Galois group of a non-Archimedean local field $F$ of…

We discuss the local Lorentz invariance in the context of N=1 supergravity and show that a previous attempt to find explicit solutions to the Lorentz constraint in terms of $\gamma-$matrices is not correct. We improve that solution by using…