On the nilradical of a parabolic subgroup
This is an article which will appear in the volume
"Symmetry In Representation Theory and Its Applications.
In honour of Nolan R. Wallach" of Progress in Mathematics,
Birkhauser.
We present various approaches to the understanding of the structure
of the nilradical of parabolic subgroups in type $A$. In particular, we
consider the complement of the open dense orbit and describe its
irreducible components.
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