Cycle Spaces of Infinite Dimensional Flag Domains
Joseph A. Wolf

TL;DR
This paper investigates the structure of cycle spaces associated with open orbits of real forms of infinite-dimensional complex groups on flag manifolds, extending finite-dimensional theories to the infinite-dimensional setting.
Contribution
It develops the theory of cycle spaces for infinite-dimensional flag domains, including real and quaternionic cases, generalizing finite-dimensional results.
Findings
Complete orbit structure for hermitian type real forms
Development of cycle space theory in infinite dimensions
Extension of finite-dimensional symmetric space results
Abstract
Let be a complex simple direct limit group, specifically , or . Let be a (generalized) flag in . If is or we suppose further that is isotropic. Let denote the corresponding flag manifold; thus where is a parabolic subgroup of . In a recent paper with Ignatyev and Penkov, we studied real forms of and properties of their orbits on . Here we concentrate on open --orbits . When is of hermitian type we work out the complete --orbit structure of flag manifolds dual to the bounded symmetric domain for . Then we develop the structure of the corresponding cycle spaces . Finally we study the real and…
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Taxonomy
TopicsAdvanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology
