Fri, 11.01.2019, 14:30

End:
Fri, 11.01.2019, 15:30
PBW and linear degeneration of flag varieties
Emmy-Noether-Seminar

Speaker: Ghislain Fourier (Aachen)
Host: F. Knop
Room: 04.363

I'll recall various interpretations of flag varieties, in terms of linear algebra, of commutative algebra, of Lie theory, of Schubert varieties. Each of these viewpoints allows to define degenerations of this projective variety. I'll introduce PBW degenerations by using the Lie theory approach and linear degenerations by using linear algebra.
The linear degenerations can be parametrized and classified by a poset, the rank sequences. Within this (finite!) poset, we identified the flat degenerations, the flat irreducible ones, the normal ones, the PBW degenerations. In the end, I'll link this poset also to degenerations coming from the commutative algebra point of view of the flag variety. This is joint work with G.Cerulli Irelli, X.Fang, E.Feigin and M.Reineke.