Related papers: Constant term of $H$-forms

Given a $p$-adic group $G$ equipped with an action of a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$, and a reductive fixed-point subgroup $G^\Gamma$, we establish a relationship between constructions of types for these two groups…

Let $G$ and $H$ be locally compact groups and consider their associate spaces of almost periodic functions $AP(G)$ and $AP(H)$. We investigate the continuous group homomorphisms induced by isometries of $AP(G)$ into $AP(H)$. Among others,…

Let G be the group of rational points of a reductive connected group over a finite field (resp. nonarchimedean local field of characteristic p) and R a commutative ring. The unipotent (resp. pro-p Iwahori) invariant functor takes a smooth…

We extend the methods of geometric invariant theory to actions of non--reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non--reductive. Given a linearization of the natural action of…

We consider a group SO(2n+1) over a p-adic field, and tempered irreducible representations of this group, of unipotent reduction. We use the construction due to Lusztig of these representations. In an old paper with Moeglin, we have defined…

A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category…

We can attach a local constant to every finite dimensional continuous complex representation of a local Galois group of a non-archimedean local field $F/\mathbb{Q}_p$ by Deligne and Langlands. Tate \cite{JT1} gives an explicit formula for…

In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the…

In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how…

Real forms of a complex reductive group are classified in terms of Galois cohomology $H^1(\Gamma,G_{ad})$ where $G_{ad}$ is the adjoint group. Alternatively, the theory of the Cartan involution gives a description in terms of cohomology…

The purpose of this paper is to investigate the non-existence of global weak solutions of the following degenerate inequality on the Heisenberg group $$ \begin{cases} u_{t}-\Delta_{\mathbb{H}}u\geq…

Let $H$ be a torsion-free $\delta$-hyperbolic group with respect to a finite generating set $S$. Let $a_1,..., a_n$ and $a_{1*},..., a_{n*}$ be elements of $H$ such that $a_{i*}$ is conjugate to $a_i$ for each $i=1,..., n$. Then, there is a…

In this paper, we discover a new noncommutative algebra. We refer this algebra as the constant term algebra of type $A$, which is generated by certain constant term operators. We characterize a structural result of this algebra by…

Let $G$ be a real reductive linear group in the Harish-Chandra class. Suppose that $P$ is a parabolic subgroup of $G$ with Langlands decomposition $P=MAN$. Let $\pi$ be an irreducible representation of the Levi factor $L=MA$. We give…

We study polynomials interpolating the (rational) constant terms of certain meromorphic modular forms for Hecke groups. We make observations about the divisibility properties of the constant terms and connect them to several sequences, for…

Let $G$ be a reductive group and $\theta$ an involution on $G$, both defined over a $p$-adic field. We provide a criterion for $G^\theta$-integrability of matrix coefficients of representations of $G$ in terms of their exponents along…

Let $p$ be a prime number and $\Bbbk=\bar{\mathbb{F}}_p$, the algebraic closure of the finite field $\mathbb{F}_p$ of $p$ elements. Let ${\bf G}$ be a connected reductive group defined over $\mathbb{F}_p$ and ${\bf B}$ be a Borel subgroup…

Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…

Let $G$ be a reductive group over a non archimedean local field, and $\psi$ a non-degenerate character of the unipotent radical $U_0$ of a minimal parabolic subgroup $P_0=M_0U_0$. For $P=MU\supseteq P_0$, we show that the descent to the…

Given a functor from any category into the category of topological spaces, one obtains a linear representation of the category by post-composing the given functor with a homology functor with field coefficients. This construction is…