Related papers: Total positivity in symmetric spaces

The present paper is devoted to the projective positivity in the category of function systems, which plays a key role in the quantization problems of the operator systems. The main result of the paper asserts that every unital star-normed…

In this paper we treat some applications of Kawamata's positivity theorem. We get a weak answer to \cite [Section 3]{KeMaMc}. And we investigate the singularities on the target spaces of some morphisms.

Within the context of piecewise linear manifolds we establish reflection positivity with a Hilbert action given in terms of the Regge curvature and a cosmological term. Using this positivity a Hilbert space for a quantum theory is…

Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.

We present sufficient conditions for total positivity of Riordan arrays. As applications we show that many well-known combinatorial triangles are totally positive and many famous combinatorial numbers are log-convex in a unified approach.

We prove that the isoperimetric constant is positive for all symmetric spaces of noncompact type and compute it explicitly.

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…

This is a survey article on the Springer correspondence for symmetric spaces. We discuss various generalization of the theory of the Springer correspondence for reductive groups to symmetric spaces and exotic symmetric spaces associated to…

This is a brief and informal introduction to cluster algebras. It roughly follows the historical path of their discovery, made jointly with A.Zelevinsky. Total positivity serves as the main motivation.

This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…

In [4], we use the root categories to realize Chevalley groups. Lusztig's theory of total positivity for reductive groups can be naturally applied to Chevalley groups. In this paper, we explicitly determine regions of $\mathbb{R}_{>0}^t$…

We identify a positivity property for partition functions in quantum systems with a unitary symmetry group, and we call this "twist positivity." The existence of Feynman-Kac measures and the existence of zero-mass limits are both related to…

The relevance that the property of complete positivity has had in the determination of quantum structures is briefly reviewed, together with recent applications to neutron optics and quantum Brownian motion. A possible useful application…

We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized characters of the symmetric group. We prove this conjecture for…

We observe that an analogue of the Positive Mass Theorem in the time-symmetric case for three-space-time-dimensional general relativity follows trivially from the Gauss-Bonnet theorem. In this case we also have that the spatial slice is…

The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.

In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of…

In this paper, we consider matrices whose entries are combinatorial sequences which can be expressed in terms of a convolution of elementary and complete homogeneous symmetric functions. We establish the total positivity of these matrices…

An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.

This is the first of a series of papers where we develop a theory of total positivity for loop groups. In this paper, we completely describe the totally nonnegative part of the polynomial loop group GL_n(\R[t,t^{-1}]), and for the formal…