Geometry Seminar

On closure of cycle spaces of flag domains

 

Dr. Jaehyun Hong
 Seoul National University
, Korea

 

 

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:

February 1, 2007 (Thursday)

Time:

4:00 – 5:00pm

Place:

Room 517, Meng Wah Complex, HKU

 

 

All are welcome