Modular reduction of nilpotent orbits
Algebra Seminar
1st October 2024, 4:00 pm – 5:00 pm
Fry Building, 2.04
The general linear group GL(n,k) over a field k acts on the space gl(n,k) of (n x n)-matrices by conjugation. The set N(gl(n,k)) of nilpotent matrices is preserved by this action and the group acts with finitely many orbits, with each orbit having a representative given by the Jordan normal form that is independent of k. In fact, more is true. The structure of the stabiliser of this nilpotent matrix is even independent of k.
The natural setting for these questions is the setting of connected reductive algebraic groups. One can ask to what extent these types of results hold for arbitrary split connected reductive groups. In this talk I will outline several reasonable ways to generalise the situation of GL(n,k), both by changing GL(n,k) and the space gl(n,k) on which it acts.
This is on-going joint work with Adam Thomas (Warwick).
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