Results 11 to 20 of about 6,919,485 (295)

Total positivity, Schubert positivity, and geometric Satake [PDF]

Journal of Algebra, 2016
Let G be a simple and simply-connected complex algebraic group, and let X in the Langlands dual group G^ be the centralizer subgroup of a principal nilpotent element.
Konstanze Rietsch, Rietsch, Konstanze, Thomas Lam, Lam, Thomas   +3 more
core   +6 more sources

Hyperdeterminantal Total Positivity

Symmetry, Integrability and Geometry: Methods and Applications
For a given positive integer , the concept of hyperdeterminantal total positivity is defined for a kernel : ℝ²ᵐ → ℝ, thereby generalizing the classical concept of total positivity.
Johnson, Kenneth W., Richards, Donald St. P.   +1 more
core   +4 more sources

Total Positivity and Convexity Preservation [PDF]

Journal of Approximation Theory, 1999
In this paper we define convexity and rational convexity preservation of systems of functions and we show that total positivity and rational convexity preservation are equivalent. We also characterize certain convexity preserving systems in terms of weak
Floater, Michael S.
core   +3 more sources

Generalizing Lusztig's total positivity

Inventiones mathematicae
Réorganisation complète du manuscrit. Beaucoup de démonstrations ont été améliorées.We introduce the notion of Θ-positivity in real simple Lie groups.
Wienhard, Anna, Guichard, Olivier
core   +6 more sources

The total positivity interval [PDF]

Linear Algebra and its Applications, 2004
If A∈Mn is totally positive (TP), we determine the maximum open interval I around the origin such that, if μ∈I, then A−μI is TP. If A is TP, μ∈I and A−μI=LU, then B defined by B−μI=UL is TP, and has the same total positivity interval I.
Gladwell, G.M.L., Ghanbari, K.
core   +3 more sources

Positive Hankel Matrices, Eigenvalues and Total Positivity

Mathematics
For positive Hankel matrices, an interval containing all eigenvalues is obtained. With a stronger condition, we also construct two sharper intervals for the eigenvalue localization. The total positivity of positive Hankel matrices is analyzed.
Juan Manuel Peña
doaj   +2 more sources

Total positivity and dependence of order statistics [PDF]

, 2023
In this comprehensive study, we delve deeply into the concept of multivariate total positivity, defining it in accordance with a direction. We rigorously explore numerous salient properties, shedding light on the nuances that characterize this notion ...
Amo Artero, Enrique de, Úbeda Flores, Manuel, Úbeda-Flores, Manuel, Quesada Molina, José Juan, Amo, Enrique de   +4 more
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The Tropical Totally Positive Grassmannian [PDF]

Journal of Algebraic Combinatorics, 2005
Tropical algebraic geometry is the geometry of the tropical semiring (R, min, +). The theory of total positivity is a natural generalization of the study of matrices with all minors positive. In this paper we introduce the totally positive part of the tropicalization of an arbitrary affine variety, an object which has the structure of a polyhedral fan.
Speyer, David, Williams, Lauren
openaire   +3 more sources

Total Positivity: Tests and Parametrizations [PDF]

The Mathematical Intelligencer, 2000
An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.
Fomin, Sergey, Zelevinsky, Andrei
openaire   +2 more sources

Total Positivity in Springer Fibres [PDF]

The Quarterly Journal of Mathematics, 2020
Abstract Let u be a unipotent element in the totally positive part of a complex reductive group. We consider the intersection of the Springer fibre at u with the totally positive part of the flag manifold. We show that this intersection has a natural cell decomposition which is part of the cell decomposition (Rietsch) of the totally ...
openaire   +3 more sources