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math.AG2018
Hessenberg varieties, Slodowy slices, and integrable systems
Hiraku Abe, Peter Crooks
This work is intended to contextualize and enhance certain well-studied relationships between Hessenberg varieties and the Toda lattice, thereby building on the results of Kostant,…
math.AG2017
Complex adjoint orbits in Lie theory and geometry
Peter Crooks
This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced…
math.AG2015
Properties of nilpotent orbit complexification
Peter Crooks
We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra and those in its complexification . In p…