Related papers: Total positivity in symmetric spaces
We study the exponential map of connected symmetric spaces and characterize, in terms of midpoints and of infinitesimal conditions, when it is a diffeomorphism, generalizing the Dixmier-Saito theorem for solvable Lie groups. We then give a…
We present an application of elimination theory to the study of singularities over arbitrary fields, particularly to the open problem of resolution. A partial extension of a function, defining resolution of singularities over fields of…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
We give a new and elementary proof showing that a homeomorphism of a compact metric space is positively expansive if and only if the space is finite.
This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
We show that string/M theory compactifications to maximally symmetric space-times using manifolds whose scalar curvature is everywhere negative, must have significant warping, large stringy corrections, or both.
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
We show that any Hermiticity and trace preserving continuous semigroup gamma_t in d dimensions is completely positive if and only if the semigroup gamma_t otimes gamma_t is positivity preserving.
This is a short note about Schur positivity. We introduce Schur polynomials and explain how they appear in the representation theory of the general linear group. We end with a new result of the author with F. Bergeron and V. Reiner that…
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.
We prove a positivity result for the T-equivariant K-theory of flag varieties associated to any symmetrizable Kac-Moody group.
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask…
We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.
Let G/H be a reductive symmetric space and K a maximal compact subgroup of G. We study Fourier transforms of compactly supported K-finite distributions on G/H and characterize the image of the space of such distributions.
We characterize symmetric spaces of non-positive curvature by the equality case of general inequalities between geometric quantities
We introduce a countable collection of positivity classes for Hermitian symmetric functions on a complex manifold, and establish their basic properties. We study a related notion of stability. The first main result shows that, if the…