Related papers: Total positivity in symmetric spaces

We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family of inner products, also providing new information on the order strucure an extreme points in some…

In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.

Using the combinatorics of $\alpha$-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that…

This article proves the existence of completely positive quasimultiplicative maps from the group algebra of imprimitive reflection groups to the set of bounded operators, and uses those linear maps to define creation and annihilation…

We initiate a careful study of a generalized symmetric imprimitivity theory for commuting proper actions of locally compact groups H and K on a C*-algebra.

We develop the basic model theory of local positive logic, a new logic that mixes positive logic (where negation is not allowed) and local logic (where models omit types of infinite distant pairs). We study several basic model theoretic…

Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is…

In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…

We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetime into two parts. These two ways of cutting the de Sitter give rise to two different spatial infinities. For spacetimes which are asymptotic to…

We extend the original Cachazo-Douglas-Seiberg-Witten conjecture for symmetric spaces.

We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…

There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…

A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…

In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.

In earlier papers the second author and Charles Read have introduced and studied a new notion of positivity for operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. The present…

Using Lusztig's total positivity in split real Lie groups V. Fock and A. Goncharov have introduced spaces of positive (framed) representations. For general semisimple Lie groups a generalization of Lusztig's total positivity was recently…

We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their…

We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In…

In this note, we unify and extend various concepts in the area of $G$-complete reducibility, where $G$ is a reductive algebraic group. By results of Serre and Bate--Martin--R\"{o}hrle, the usual notion of $G$-complete reducibility can be…

An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.