Related papers: Global Parabolic Induction and Abstract Automorphi…
Let $G_n$ be an inner form of a general linear group over a non-Archimedean field. We fix an arbitrary irreducible representation $\sigma$ of $G_n$. Lapid-M\'inguez give a combinatorial criteria for the irreducibility of parabolic induction…
In this paper, we explicitly determine the local $2$-adic component of a non-selfdual automorphic representation $\Pi$ of $\mathrm{GL}_3$ constructed by van Geemen and Top. We prove that $\Pi_2$ is a parabolically induced representation of…
This is an expanded version of the text ``Perverse Sheaves on Loop Grassmannians and Langlands Duality'', AG/9703010. The main new result is a topological realization of algebraic representations of reductive groups over arbitrary rings. We…
We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form…
In this paper we prove the Geyer-Jarden conjecture on the torsion part of the Mordell-Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic. The class consists of all abelian…
We give a universal construction of a derived affine group scheme and its representation category from a symmetric monoidal infinity-category, which we shall call the tannnakization of a symmetric monoidal infinity-category. This can be…
This is an updated version of ANT-0253. Let F be a number field with absolute Galois group G. We associate, to each continuous, solvable C-representation of G of GO(4)-type, an automorphic form P of GL(4)/F with the same L-function. As a…
This paper exposes the underlying mechanism for obtaining second integral moments of $GL_2$ automorphic $L$--functions over an arbitrary number field. Here, moments for $GL_2$ are presented in a form enabling application of the structure of…
We present a general conjecture on congruences between Hecke eigenvalues of parabolically induced and cuspidal automorphic representations of split reductive groups, modulo divisors of critical values of certain $L$-functions. We examine…
We study the p-adic analogue of the arithmetic Gan-Gross-Prasad (GGP) conjectures for unitary groups. Let $\Pi$ be a conjugate-selfdual cuspidal automorphic representation of GL_{n} x GL_{n+1} over a CM field, which is algebraic of minimal…
Let $G$ be a reductive group over a number field $F$, which is split at a finite place $\mathfrak{p}$ of $F$, and let $\pi$ be a cuspidal automorphic representation of $G$, which is cohomological with respect to the trivial coefficient…
The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence. Our construction is based on the study of certain relative compactification of the moduli stack of…
We construct new irreducible components in the discrete automorphic spectrum of symplectic groups. The construction lifts a cuspidal automorphic representation of $\mathrm{GL}_{2n}$ with a linear period to an irreducible component of the…
We consider an oriented version of the stable symplectic category defined in \cite{N}. We show that the group of monoidal automorphisms of this category, that fix each object, contains a natural subgroup isomorphic to the solvable quotient…
This article studies automorphism groups of graph products of arbitrary groups. We completely characterise automorphisms that preserve the set of conjugacy classes of vertex groups as those automorphisms that can be decomposed as a product…
Given a supercuspidal representation $\sigma$ of a parabolic subgroup $P$ of reductive group $G$, we discover a universal hierarchical structure of reducibility of the parabolic induction $Ind^G_P(\sigma)$, i.e. always irreducible from some…
In this paper, we show that, under certain assumptions, a parabolic induction $Ind_B^G\lambda$ from the Borel subgroup $B$ of a (real or $p$-adic) reductive group $G$ decomposes into a direct sum of the form: \[ Ind_B^G\lambda =…
We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…
We study in this paper Hida's p-adic Hecke algebra for GL_n over a CM field F. Hida has made a conjecture about the dimension of these Hecke algebras, which he calls the non-abelian Leopoldt conjecture, and shown that his conjecture in the…
In this paper we introduce a class of `parabolic' subgroups for the generalized braid group associated to an arbitrary irreducible complex reflection group, which maps onto the collection of parabolic subgroups of the reflection group.…