Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 3 (2019), 451-462.

Nilpotent orbits for Borel subgroups of $\mathrm{SO}_{5}(k)$

Madeleine Burkhart and David Vella

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Let G be a quasisimple algebraic group defined over an algebraically closed field  k and B a Borel subgroup of G acting on the nilradical n of its Lie algebra b via the adjoint representation. It is known that B has only finitely many orbits in only five cases: when G is type A n for n 4 , and when G is type B 2 . We elaborate on this work in the case when G = SO 5 ( k ) (type B 2 ) 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.

Article information

Involve, Volume 12, Number 3 (2019), 451-462.

Received: 16 August 2017
Revised: 8 February 2018
Accepted: 10 July 2018
First available in Project Euclid: 5 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B08: Coadjoint orbits; nilpotent varieties 20G05: Representation theory

nilpotent orbits Borel subgroups modality


Burkhart, Madeleine; Vella, David. Nilpotent orbits for Borel subgroups of $\mathrm{SO}_{5}(k)$. Involve 12 (2019), no. 3, 451--462. doi:10.2140/involve.2019.12.451.

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