ABSTRACT
This chapter shows how to construct new nilpotent orbits from old ones, following Lusztig and Spaltenstein. It also shows that every nilpotent orbit sln in is induced from the 0 orbit in some Levi subalgebra and give a formula for the partition of any induced orbit. The chapter gives a simple partition criterion due to Kempken and Spaltenstein for a classical orbit to be rigid. It points out that every nilpotent orbit in sln is a Richardson orbit. This is a result of Ozeki and Wakimoto; the chapter follows the exposition in Kraft's paper. Kraft actually gives a formula for the partition of any Richardson orbit in sln; he then observes that any nilpotent orbit can occur on the right-hand side of his formula. Following The chapter generalizes the results to give a formula for the partition of any induced orbit in a classical algebra g, and derives a partition criterion for a classical nilpotent orbit to be rigid.
