Abstract
Let be a quasisimple algebraic group defined over an algebraically closed field and a Borel subgroup of acting on the nilradical of its Lie algebra via the adjoint representation. It is known that has only finitely many orbits in only five cases: when is type for , and when is type . We elaborate on this work in the case when (type ) by finding the defining equations of each orbit. We use these equations to determine the dimension of the orbits and the closure ordering on the set of orbits. The other four cases, when $G$ is type $A_n$, can be approached the same way and are treated in a separate paper.
Citation
Madeleine Burkhart. David Vella. "Nilpotent orbits for Borel subgroups of $\mathrm{SO}_{5}(k)$." Involve 12 (3) 451 - 462, 2019. https://doi.org/10.2140/involve.2019.12.451
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