Related papers: Elements of Automorphic Representations

We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…

We prove the Ramanujan-Petersson conjecture for Maass forms of the group $SL(2,Z)$, with the help of automorphic distribution theory and pseudodifferential analysis. The first notion is an alternative to classical automorphic function…

Let $F_n$ be the free group on $n\ge 2$ elements and $\A(F_n)$ its group of automorphisms. In this paper we present a rich collection of linear representations of $\A(F_n)$ arising through the action of finite index subgroups of it on…

The main aim of this article is to develop, in a fully detailed fashion, a {\bf unified} theory of the spectral theory of mean values of individual automorphic L-functions which is a natural extension of the fourth moment of the Riemann…

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

For a rational map $\phi$ from a metric graph $\varGamma$ to a tropical projective space $\boldsymbol{TP^n}$ defined by a ratio of rational functions $f_1, \ldots, f_{n + 1}$, an automorphism $\sigma$ of $\varGamma$ induces a permutation of…

We develop an explicit algebriac de Rham theory for relative completion of $\mathrm{SL}_2(\mathbb{Z})$. This allows the construction of iterated integrals involving modular forms of the second kind, generalizing iterated integrals of…

We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines $\Gamma$-spaces and framed…

We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.

We use modular symbols to construct p-adic L-functions for cohomological cuspidal automorphic representations on GL(2n), which admit a Shalika model. Our construction differs from former ones in that it systematically makes use of the…

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…

The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…

In this note, we consider models in $\mathbb C^2$. The purpose of this note is twofold. We first show a characterization of models in $\mathbb C^2$ by their noncompact automorphism groups. Then we give an explicit description for…

This paper investigates simple $3$-$(2^n+1,13,\lambda)$ designs admitting $\mathrm{PSL}$$(2,2^n)$ as an automorphism group. We determine all possible values of $\lambda$ by systematically analyzing the orbits of $13$-element subsets under…

In this paper we consider the very wide class of varieties of representations of Lie algebras over the field k, which has characteristic 0. We study the relation between the geometric equivalence and automorphic equivalence of the…

We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split…

Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides the quantization of the algebra of functions on the…

We utilize the structure of quasiautomorphic forms over an arbitrary Hecke triangle group to define a new vector analogue of an automorphic form. We supply a proof of the functional equations that hold for these functions modulo the group…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…

We describe some recent developments and formulate some conjectures in the genuine representation theory and the study of automorphic forms of the metaplectic group $\mathrm{Mp}(2n)$, from the point of view of the theta correspondence as…