Related papers: Solid locally analytic representations of $p$-adic…
In this article, we propose a $p$-adic analogue of complex Hilbert space and consider generalizations of some well-known theorems from functional analysis and the basic study of operators on Hilbert spaces. We compute the $K$-theory of the…
We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…
We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…
We define a reduction covariant for the representations a la Vinberg associated to stably graded Lie algebras. We then give an analogue of the LLL algorithm for the odd split special orthogonal group and show how this can be combined with…
In this paper we analyse the topological group cohomology of finite-dimensional Lie groups. We introduce a technique for computing it (as abelian groups) for torus coefficients by the naturally associated long exact sequence. The upshot in…
In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie algebras and some of their strong homotopy analogues. Then…
We investigate $p$-adic cohomologies of log rigid analytic varieties over a $p$-adic field. For a log rigid analytic variety $X$ defined over a discretely valued field, we compute the Kummer pro-\'etale cohomology of…
We study a compact invariant convex set $E$ in a polar representation of a compact Lie group. Polar rapresentations are given by the adjoint action of $K$ on $\mathfrak{p}$, where $K$ is a maximal compact subgroup of a real semisimple Lie…
Meta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with…
In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and…
We study analogues of Cartan decompositions of Lie groups for totally disconnected locally compact groups. It is shown using these decompositions that a large class of totally disconnected locally compact groups acting on trees and…
We show via an application of techniques from complex interpolation theory how the $L^p$-pseudofunction algebras of a locally compact group $G$ can be understood as sitting between $L^1(G)$ and $C^*(G)$. Motivated by this, we collect and…
Starting from a topological treatment of the Eisenstein class of a torus bundle, we define log-rigid analytic classes for $\mathrm{SL}_n(\mathbb{Z})$. These are group cohomology classes for $\mathrm{SL}_n(\mathbb{Z})$ valued on log-rigid…
This Ph.D. thesis belongs to the realm of mod $p$ representation theory of $p$-adic groups. The main object of study is the inner form of the general linear group $\mathrm{GL}(m,D)$ where $D$ is a division algebra over a non-Archimedean…
A weakly complete vector space over $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$ is isomorphic to $\mathbb{K}^X$ for some set $X$ algebraically and topologically. The significance of this type of topological vector spaces is…
We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…
In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some…
In the first part of my talk I will explain a solution to the extension of Lie's problem on classification of "local continuous transformation groups of a finite-dimensional manifold" to the case of supermanifolds. (More precisely, the…
Let G be a compact, locally L-analytic group, where L is a finite extension of Qp. Let K be a discretely valued extension field of L. We study the algebra D(G,K) of K-valued locally analytic distributions on G, and apply our results to the…
In this short paper, we give a $p$-adic analogue of the Hard Leftschetz Theorem.