Browsing by Author "Baur, Karin"
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- ItemOn the Complement of the dense orbit for a quiver of type A(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Baur, Karin; Hille, LutzLet At be the directed quiver of type A with t vertices. For each dimension vector d there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank conditions to define the irreducible components in the complement of the dense orbit. Then we compare this result with already existing ones by Knight and Zelevinsky, and by Ringel. Moreover, we compare with the fan associated to the quiver A and derive a new formula for the number of orbits using nilpotent classes. In the complement of the dense orbit we determine the irreducible components and their codimension. Finally, we consider several particular examples.
- ItemOn the Complement of the Richardson Orbit(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Baur, Karin; Hille, LutzWe consider parabolic subgroups of a general algebraic group over an algebraically closed field k whose Levi part has exactly t factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup P has an open dense P-orbit. In the complement to this dense orbit, there are infinitely many orbits as soon as the number t of factors in the Levi part is > 6. In this paper, we describe the irreducible components of the complement. In particular, we show that there are at most t − 1 irreducible components. We are also able to determine their codimensions.