Related papers: On Rigidity of $S$-Arithmetic Kac-Moody Groups

We establish sharp Sobolev embedding properties within a broad class of compact matrix quantum groups of Kac type under the polynomial growth or the rapid decay property of their duals. Main examples are duals of polynomially growing…

In this paper, some generalized metric properties in strongly topological gyrogroups are studied.

We define Tits rigidity for visual boundaries of CAT(0) groups, and prove that the join of two Cantor sets and its suspension are Tits rigid.

We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed…

We prove the finiteness of formal analogues of the spherical function (Spherical Finiteness), the ${\mathbf c}$-function (Gindikin-Karpelevich Finiteness), and obtain a formal analogue of Harish-Chandra's limit (Approximation Theorem)…

We introduce the notion of rigidity for automorphic representations of groups over global function fields. We construct the Langlands parameters of rigid automorphic representations explicitly as local systems over open curves. We expect…

In this paper we determine the rational homotopy type of the classifying space of a generic Kac-Moody group by computing its rational cohomology ring. As an application we determine the rational homology Hopf algebra of the generic…

Several rigidity problems in toric topology are addressed in \cite{ma-su08}. In this paper, we survey results on those problems including recent development.

We prove rigidity facts for groups acting on pseudo-Riemannian manifolds by preserving unparameterized geodesics.

A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…

We prove a rigidity theorem for the geometry of the unit ball in random subspaces of the scl norm in B_1^H of a free group. In a free group F of rank k, a random word w of length n (conditioned to lie in [F,F]) has scl(w)=log(2k-1)n/6log(n)…

Arithmetic groups are groups of matrices with integral entries. We shall first discuss their origin in number theory (Gauss, Minkowski) and their role in the "reduction theory of quadratic forms". Then we shall describe these groups by…

In this article, we study deformations of conjugate self-dual Galois representations. The study has two folds. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,…

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

We introduce geometric and homological finiteness properties for countable approximate groups via coarse geometry and then study these finiteness properties for S-arithmetic reductive approximate groups. For S-arithmetic approximate groups…

In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.

In this note we give a detailed proof of certain results on geometry of numbers in the $S$-adic case. These results are well-known to experts, so the aim here is to provide a convenient reference for the people who need to use them.

We prove a strong rigidity property of the Heisenberg groups, that is, they can be distinguished from any other 1-connected Lie groups via their unitary dual spaces, in particular via the Morita equivalence class of their group…

We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on…

We create plots of algebraic integers in the complex plane, exploring the effect of sizing the integers according to various arithmetic invariants. We focus on Galois theoretic invariants, in particular creating plots which emphasize…