On closure of cycle spaces of flag domains
Dr.
Seoul National University
Abstract
A flag domain is an open orbit D of a noncompact
real form G0 acting on a
flag manifold of a semisimple complex Lie group G. Given D and a maximal compact subgroup K0 of G0,
there is a unique complex K0-orbit
C0 in D which is regarded as a point in the (full) cycle space of q-dimensional cycles in D.
The group theoretical cycle space is defined
by the connected component containing C0
of the intersection of the G -orbit
of C0 with the full cycle
space. In this talk we will show that that the group theoretical cycle space is
closed in the full cycle space. Thus the group theoretical cycle space is a
connected component of the full cycle space containing C0 if they have the same dimension.
This
result follows from an analysis of the closure of the universal domain in any G -equivariant
compactification of the affine symmetric space G/K,
where K is the complexification
of K0 in G. This is a joint work with A.
Huckleberry.
Date: |
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Time: |
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Place: |
Room 517, Meng Wah Complex, HKU |
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All are
welcome |
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