Related papers: On probabilistic identities and coset identities i…

This note identifies compact and {\sigma}-compact subsets of probability measures on a class of metric spaces with respect to the weak convergence topology. Moreover, it is shown by an example, that the space of probability measures on a…

In previous papers we formulated an analogue of the Ichino--Ikeda conjectures for Whittaker--Fourier coefficients of automorphic forms on classical group and the metaplectic group. In the latter case we reduced the conjecture to a local…

Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper…

We construct $p$-adic analogs of operator colligations and their characteristic functions. Consider a $p$-adic group $G=GL(\alpha+k\infty, Q_p)$, its subgroup $L=O(k\infty,Z_p)$, and the subgroup $K=O(\infty,Z_p)$ embedded to $L$…

Let G be a finite group. The Plesken Lie algebra L[G] is a subalgebra of the complex group algebra C[G] and admits a direct-sum decomposition into simple Lie algebras based on the ordinary character theory of G. In this paper we review the…

We investigate some properties of the $p$-elements of a profinite group $G$. We prove that if $p$ is odd and the probability that a randomly chosen element of $G$ is a $p$-element is positive, then $G$ contains an open prosolvable subgroup.…

Let $G$ be a compact $p$-adic analytic group with no element of order $p$ and $H$ be its maximal uniform normal subgroup. Let $K$ be a finite extention of $\mathbb{Q}_p$. We show that the Grothendieck group of the completion of the algebra…

For any prime $p$ and group $G$, denote the pro-$p$ completion of $G$ by $\hat{G}^p$. Let $\mathcal{C}$ be the class of all groups $G$ such that, for each natural number $n$ and prime number $p$, $H^n(\hat{G^p},\mathbb Z/p)\cong H^n(G,…

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally…

The purpose of this paper is to study resolutions of locally analytic representations of a $p$-adic reductive group $G$. Given a locally analytic representation $V$ of $G$, we modify the Schneider-Stuhler complex (originally defined for…

For a Poisson manifold $M$ we develop systematic methods to compute its Picard group $Pic(M)$, i.e., its group of self Morita equivalences. We establish a precise relationship between $Pic(M)$ and the group of gauge transformations up to…

We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This…

Let G be a connected split reductive group over a p-adic field. In the first part of the paper we prove, under certain assumptions on G and the prime p, a localization theorem of Beilinson-Bernstein type for admissible locally analytic…

A well known notion of $k$-rectifiable set can be formulated in any metric space using Lipschitz images of subsets of $\mathbb{R}^k$. We prove some characterizations of $k$-rectifiability, when the metric space is an arbitrary homogeneous…

We extend a theorem of Haagerup and Kraus in the C*-algebra context: for a locally compact group with the approximation property (AP), the reduced C*-crossed product construction preserves the strong operator approximation property (SOAP).…

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…

We compare the Pontryagin duals of fine Selmer groups of two congruent $p$-adic Galois representations over admissible pro-$p$, $p$-adic Lie extensions $K_\infty$ of number fields $K$. We prove that in several natural settings the…

We prove that if an analytic subset $A$ of a linear metric space $X$ is not contained in a $\sigma Z_\omega$-subset of $X$ then for every Polish convex set $K$ with dense affine hull in $X$ the sum $A+K$ is non-meager in $X$ and the sets…

A discrete subset $S$ of a topological group $G$ is called a {\it suitable set} for $G$ if $S\cup \{e\}$ is closed in $G$ and the subgroup generated by $S$ is dense in $G$, where $e$ is the identity element of $G$. In this paper, the…

Dahmen and Schmeding have obtained the result that although the smooth Lie group $G$ of real analytic diffeomorphisms $\mathbb S^{\,1.}\to\mathbb S^{\,1.}$ has a compatible analytic manifold structure, it does not make $G$ a real analytic…