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Tesi etd-06262018-121559


Tipo di tesi
Tesi di laurea magistrale
Autore
CARMASSI, MICHELE
URN
etd-06262018-121559
Titolo
On the orbits of the Borel subgroup on the abelian nilradical
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Maffei, Andrea
Parole chiave
  • characteristic 2
  • dimension
  • minimal parabolic subgroups
Data inizio appello
13/07/2018
Consultabilità
Completa
Riassunto
Let G be a connected, reductive, linear algebraic group and B ⊆ G a Borel subgroup containing a maximal torus T . Suppose P ⊇ B a parabolic subgroup with Levi decom- position P = L Ru(P ) where the unipotent radical Ru(P ) is abelian. In a recent paper A.Maffei and J.Gandini proved a parametrization of the B-orbits on the Lie algebra p u of Ru(P ) and a combinatorial characterization of the Bruhat order on such orbits when the underlying field is not of characteristic 2.
In this thesis, we will study the same problem in the caracteristic 2 case. At first, we will show that, if the root system of G is simply laced, both the parametrization and the characterization still hold in the same form. Then, we will study the problem in the case of root system of type B and C, where we will show a different parametrization of the B-orbits and, in the type B case, a different characterization of the Bruhat order.
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