Related papers: On bi-invariant word metrics
We prove that finite index subgroups in S-arithmetic Chevalley groups are bounded.
We prove that the width of any word in a simply connected Chevalley group of rank at least 2 over the ring that is a localisation of the ring of integers in a number field is bounded by a constant that depends only on the root system and on…
We study biinvariant word metrics on groups. We provide an efficient algorithm for computing the biinvariant word norm on a finitely generated free group and we construct an isometric embedding of a locally compact tree into the biinvariant…
We study invariant and bi-invariant metrics on groups focusing on finite groups $G$. We show that non-equivalent (bi) invariant metrics on $G$ are in 1-1 correspondence with unitary symmetric (conjugate) partitions on $G$. To every metric…
In this paper, we construct infinitely many bi-invariant metrics on the Hamiltonian diffeomorphism group and study their basic properties and corresponding generalizations of the Hofer inequality and Sikorav one.
We prove that a homomorphism between free groups of finite rank equipped with the bi-invariant word metrics is a quasi-isometry if and only if it is an isomorphism.
We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for…
We generalize Chevalley's theorem about restriction of \mathfrak{g}-invariant polynomial functions \mathfrak{g}->C to W-invariant functions on the Cartan \mathfrak{h}->C. We consider the case when \mathfrak{g} is replaced by a quantum group…
A group is said to be bounded if it has a finite diameter with respect to any bi-invariant metric. In the present paper we discuss boundedness of various groups of diffeomorphisms.
We establish a theorem concerning the commuting scheme in characteristic p. As a significant application of this theorem, we derive an explicit lower bound for the characteristic p, ensuring the validity of the higher-dimensional Chevalley…
This paper is concerned with the diameter of certain word norms on S-arithmetic split Chevalley groups. Such groups are well known to be boundedly generated by root elements. We prove that word metrics given by conjugacy classes on…
We prove ultradifferentiable Chevelley restriction theorems for a wide range of ultradifferentiable classes. As a special case we find that isotropic functions, i.e., functions defined on the vector space of real symmetric matrices…
We show that the Aut-invariant word norm on right angled Artin and right angled Coxeter groups is unbounded (except in few special cases). To prove unboundedness we exhibit certain characteristic subgroups. This allows us to find unbounded…
We pursue various restricted variable generalizations of the Chevalley-Warning theorem for low degree polynomial systems over a finite field. Our first such result involves variables restricted to Cartesian products of the Vandermonde…
We obtain simple proofs of certain inequalites for bivariate means.
We prove a higher-dimensional Chevalley restriction theorem for orthogonal groups, which was conjectured by Chen and Ng\^{o} for reductive groups. In characteristic $p>2$, we also prove a weaker statement. In characteristic $0$, the theorem…
In the spirit of an earlier result of M\"uller on the Heisenberg group we prove a restriction theorem on a certain class of two step nilpotent Lie groups. Our result extends that of M\"uller also in the framework of the Heisenberg group.
We prove that the autonomous norm on the group of compactly supported Hamiltonian diffeomorphisms of the standard $\mathbf{R}^{2n}$ is bounded.
Gromov asked if the bi-invariant metrics on a compact Lie group are extremal compared to any other metrics. In this note, we prove that the bi-invariant metrics on a compact connected semi-simple Lie group $G$ are extremal (in fact rigid)…
We prove existence of an invariant measure on a hypergroup.