JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 2, Pages 301 - 313
(August 2003)
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FIXED
POINTS OF UNIPOTENT GROUP ACTIONS IN BRUHAT
CELLS OF A FLAG MANIFOLD
Barbara A. Shipman (U. S. A.)
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Abstract: Let U be the unipotent
radical of the centralizer of a regular Jordan
canonical matrix in Sl(n,
C).
U
acts on the flag manifold Sl(n,
C)/ B (where B is the upper triangular
subgroup). In each Bruhat cell, the fixed-point
set of U consists of one or more
irreducible components, each of which is
diffeomorphic to Cq
for some q. We give an algorithm for
writing down explicitly, in terms of canonical
coordinates, the components of the fixed-point
set of U in a given Bruhat cell. |
Keywords and phrases: unipotent, flag manifold, fixed points,
Bruhat cell. |
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