Fri, 23 Feb 2024
12:00 - 13:00
Quillen Room
Dylan Johnston
University of Warwick
We say an element X in a Lie algebra g is nilpotent if ad(X) is a nilpotent operator. It is known that G_{ad}-orbits of nilpotent elements of a complex semisimple Lie algebra g are in 1-1 correspondence with Lie algebra homomorphisms sl2 -> g, which are in turn in 1-1 correspondence with Lie group homomorphisms SL2 -> G.
Thus, we may denote the homogeneous space obtained by quotienting G by the image of a Lie group homomorphism SL2 -> G by X_v, where v is a nilpotent element in the corresponding G_{ad}-orbit.
In this talk we introduce some algebraic tools that one can use to attempt to classify the homogeneous spaces, X_v, up to homotopy equivalence.
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