scholarly journals Infinite-Dimensional Nonpositively Curved Symmetric Spaces of Finite Rank

2012 ◽  
Vol 2013 (7) ◽  
pp. 1578-1627 ◽  
Author(s):  
Bruno Duchesne
Keyword(s):  
Finite Rank ◽  
Symmetric Spaces ◽  
Infinite Dimensional ◽  
Nonpositively Curved

TOWARD SYMMETRIC SPACES OF AFFINE KAC–MOODY TYPE

2006 ◽  
Vol 03 (05n06) ◽  
pp. 881-898 ◽  
Author(s):  
ERNST HEINTZE
Keyword(s):  
Fixed Point ◽  
Lie Groups ◽  
Symmetric Spaces ◽  
Point Group ◽  
Infinite Dimensional ◽  
Simple Lie Groups ◽  
Finite Dimensional ◽  
Expository Article

In this expository article we discuss some ideas and results which might lead to a theory of infinite dimensional symmetric spaces [Formula: see text] where [Formula: see text] is an affine Kac–Moody group and [Formula: see text] the fixed point group of an involution (of the second kind). We point out several striking similarities of these spaces with their finite dimensional counterparts and discuss their geometry. Furthermore we sketch a classification and show that they are essentially in 1 : 1 correspondence with hyperpolar actions on compact simple Lie groups.

JORDAN SYMMETRIC SPACES

2009 ◽  
Vol 02 (03) ◽  
pp. 407-415
Author(s):  
Cho-Ho Chu
Keyword(s):  
Symmetric Spaces ◽  
Hermitian Symmetric Spaces ◽  
Triple Systems ◽  
Infinite Dimensional ◽  
Jordan Triple Systems ◽  
Riemannian Symmetric Spaces

We introduce a class of Riemannian symmetric spaces, called Jordan symmetric spaces, which correspond to real Jordan triple systems and may be infinite dimensional. This class includes the symmetric R-spaces as well as the Hermitian symmetric spaces.

scholarly journals VARIATIONS OF BPS STRUCTURE AND A LARGE RANK LIMIT

2019 ◽  
pp. 1-33 ◽  
Author(s):  
Jacopo Scalise ◽  
Jacopo Stoppa
Keyword(s):  
Partition Function ◽  
Differential Equations ◽  
Finite Rank ◽  
Large Rank ◽  
Infinite Dimensional ◽  
Positive Degree

We study a class of flat bundles, of finite rank$N$, which arise naturally from the Donaldson–Thomas theory of a Calabi–Yau threefold$X$via the notion of a variation of BPS structure. We prove that in a large$N$limit their flat sections converge to the solutions to certain infinite-dimensional Riemann–Hilbert problems recently found by Bridgeland. In particular this implies an expression for the positive degree, genus 0 Gopakumar–Vafa contribution to the Gromov–Witten partition function of$X$in terms of solutions to confluent hypergeometric differential equations.

scholarly journals Localization and computation in an approximation of eigenvalues

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 75-81
Author(s):  
S.V. Djordjevic ◽  
G. Kantún-Montiel
Keyword(s):  
Hilbert Spaces ◽  
Finite Rank ◽  
Vector Spaces ◽  
Dimensional Case ◽  
Dimensional Vector ◽  
Infinite Dimensional ◽  
Weyl Spectrum ◽  
Isolated Points ◽  
Isolated Point ◽  
Different Parts

In this note we consider the problem of localization and approximation of eigenvalues of operators on infinite dimensional Banach and Hilbert spaces. This problem has been studied for operators of finite rank but it is seldom investigated in the infinite dimensional case. The eigenvalues of an operator (between infinite dimensional vector spaces) can be positioned in different parts of the spectrum of the operator, even it is not necessary to be isolated points in the spectrum. Also, an isolated point in the spectrum is not necessary an eigenvalue. One method that we can apply is using Weyl?s theorem for an operator, which asserts that every point outside the Weyl spectrum is an isolated eigenvalue.

scholarly journals Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

2003 ◽  
Vol 97 (3) ◽  
pp. 471-493 ◽  
Author(s):  
Leonid Faybusovich ◽  
Takashi Tsuchiya
Keyword(s):  
Finite Rank ◽  
Jordan Algebras ◽  
Infinite Dimensional ◽  
Primal Dual
Sign in / Sign up

Export Citation Format

Share Document