Related papers: Analogs of complementary series for CAT(-1) groups
We review known real forms of the quantum orthogonal groups SO_q(N). New *-conjugations are then introduced and we contruct all real forms of quantum orthogonal groups. We thus give an RTT formulation of the *-conjugations on SO_q(N) that…
Weakly-irreducible not irreducible subalgebras of $\so(1,n+1)$ were classified by L. Berard Bergery and A. Ikemakhen. In the present paper a geometrical proof of this result is given. Transitively acting isometry groups of Lobachevskian…
We extend the operations of shorting and parallel addition from the cone of bounded nonnegative selfadjoint operators in a Hilbert space to the set of all nonnegative selfadjoint linear relations. New properties of these operations and…
We work in a first-order setting where structures are spread out over a metric space, with quantification allowed only over bounded subsets. Assuming a doubling property for the metric space, we define a canonical {\em core} $\mathcal{J}$…
This paper is a more succinct version of the author's 1993 UCLA mathematics thesis. It proves that any group quasi-isometric to the product of the hyperbolic plane with the real line is a finite extension of a cocompact lattice in either…
The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with…
In this paper we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish necessary and sufficient conditions for the group to be…
The class of coarsely convex spaces is a coarse geometric analogue of the class of nonpositively curved Riemannian manifolds. It includes Gromov hyperbolic spaces, CAT(0) spaces, proper injective metric spaces and systolic complexes. It is…
The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
We study actions of compact quantum groups on type I factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz' results concerning Peter-Weyl theory for…
The quantum analogues of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indiceswe construct a quantum Minkowsky metric. In this framework, we show explicitely the correspondance…
We show that cocompact lattices in rank one simple Lie groups of non-compact type distinct from SO(2m,1) (m>0) contain surface subgroups.
In this paper we study certain groups of bilipschitz maps of the boundary minus a point of a negatively curved space that is an abelian-by-cyclic solvable Lie group, where the extension is given by a matrix whose eigenvalues all lie outside…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize 2-dimensional CAT(0) cube complexes and are a square analog of systolic complexes. We introduce and study…
We consider the following class of unitary representations $\pi $ of some (real) Lie group $G$ which has a matched pair of symmetries described as follows: (i) Suppose $G$ has a period-2 automorphism $\tau $, and that the Hilbert space…
Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the…