### The differences between unipotent orbits of classical algebraic groups and the nilpotent orbits of their Lie algebras

Algebra Seminar

23rd November 2022, 2:30 pm – 3:30 pm

Fry Building, 2.04

Let G be a classical algebraic group, and take g to be its Lie algebra. There is a Springer isomorphism from the variety of unipotent elements in G to the variety of nilpotent elements in g. Hence it is natural to consider to what extent results which hold for nilpotent elements in g hold for unipotent elements in G. In this talk I will discuss when there is a unique sl_2-subalgebra for a given nilpotent orbit in g, and compare this to when there is a unique SL_2-subgroup for a given unipotent orbit in G.

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