ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

Tesi etd-02252022-191017


Tipo di tesi
Tesi di dottorato di ricerca
Autore
CARMASSI, MICHELE
URN
etd-02252022-191017
Titolo
The B-orbits on a Hermitian symmetric variety: the characteristic 2 case and the Bruhat G-order
Settore scientifico disciplinare
MAT/02
Corso di studi
MATEMATICA
Relatori
tutor Prof. Maffei, Andrea
Parole chiave
  • Bruhat G-order
  • Hermitian symmetric varieties
  • Bruhat order
  • linear algebraic group
  • local system
  • orbits
  • KLV polynomials
Data inizio appello
02/03/2022
Consultabilità
Non consultabile
Data di rilascio
02/03/2025
Riassunto
Let G be a connected reductive linear algebraic group over an algebraically closed field. Fix a torus T and a Borel subgroup B and suppose there is a parabolic subgroup P such that G/L is a Hermitian symmetric variety.
The Borel subgroup B acts on G/L with a finite number of orbits. The set of these orbits can be ordered
through the Bruhat order.
We give parametrizations for the B-orbits in cases where the base field has characteristic 2.
We also give a characterization for the Bruhat order among these orbits and a formula to compute the dimension.

Consider now the same situation over the complex field and for every B-orbit the set of B-equivariant rank 1 local systems up to isomorphisms.
Following Lusztig and Vogan we can order the pairs orbit-local system through the Bruhat G-order.
We will show a combinatorial characterization of the Bruhat G-order. This can be used to improve the computation of the Kazhdan-Lusztig-Vogan polynomial.
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