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Displaying 41 – 60 of 73

On the structure theory of the Iwasawa algebra of a p-adic Lie group

Otmar Venjakob (2002)

Journal of the European Mathematical Society

This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, $Λ$ of a $p$ -adic analytic group $G$ . For $G$ without any $p$ -torsion element we prove that $Λ$ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null $Λ$ -module. This is classical when $G = ℤ_{p}^{k}$ for some integer $k \geq 1$ , but was previously unknown in the non-commutative case. Then the category of $Λ$ -modules...

On the verbal width of finitely generated pro- $p$ groups.

A Jaikin-Zapirain (2008)

Revista Matemática Iberoamericana

$p$ -adic Whittaker functions and vector bundles on flag manifolds

Mark Reeder (1993)

Compositio Mathematica

Principal series representations of special unitary groups over local fields

David Keys (1984)

Compositio Mathematica

Proof of a Conjecture of Bernstein.

Marko Tadic (1985)

Mathematische Annalen

Quantizations and symbolic calculus over the $p$ -adic numbers

Shai Haran (1993)

Annales de l'institut Fourier

We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the $p$ -adic numbers. We apply this theory to the study of elliptic operators over the $p$ -adic numbers and determine their asymptotic spectral behavior.

Quelques questions sur les intégrales orbitales unipotentes et les algèbres de Hecke

Jean-Loup Waldspurger (1996)

Bulletin de la Société Mathématique de France

Random walks on the affine group of local fields and of homogeneous trees

Donald I. Cartwright, Vadim A. Kaimanovich, Wolfgang Woess (1994)

Annales de l'institut Fourier

The affine group of a local field acts on the tree $𝕋 (𝔉)$ (the Bruhat-Tits building of $GL (2, 𝔉)$ ) with a fixed point in the space of ends $\partial 𝕋 (F)$ . More generally, we define the affine group $Aff (𝔉)$ of any homogeneous tree $𝕋$ as the group of all automorphisms of $𝕋$ with a common fixed point in $\partial 𝕋$ , and establish main asymptotic properties of random products in $Aff (𝔉)$ : (1) law of large numbers and central limit theorem; (2) convergence to $\partial 𝕋$ and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...

Reducibility of Unramified Unitary Principal Series Representations of p-Adic Groups and Class-1 Representations.

D. Keys (1982)

Mathematische Annalen

Representation growth of linear groups

Michael Larsen, Alexander Lubotzky (2008)

Journal of the European Mathematical Society

Let $Γ$ be a group and $r_{n} (Γ)$ the number of its $n$ -dimensional irreducible complex representations. We define and study the associated representation zeta function $𝒵_{Γ} (s) = \sum_{n = 1}^{\infty} r_{n} (Γ) n^{- s}$ . When $Γ$ is an arithmetic group satisfying the congruence subgroup property then $𝒵_{Γ} (s)$ has an “Euler factorization”. The “factor at infinity” is sometimes called the “Witten zeta function” counting the rational representations of an algebraic group. For these we determine precisely the abscissa of convergence. The local factor at a finite place...