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Tesi etd-06262018-121559


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