Tipo di tesi
Tesi di laurea magistrale
Titolo
On the orbits of the Borel subgroup on the abelian nilradical
Corso di studi
MATEMATICA
Parole chiave
- characteristic 2
- dimension
- minimal parabolic subgroups
Data inizio appello
13/07/2018
Riassunto (Italiano)
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.
