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2019 Nilpotent orbits for Borel subgroups of $\mathrm{SO}_{5}(k)$
Madeleine Burkhart, David Vella
Involve 12(3): 451-462 (2019). DOI: 10.2140/involve.2019.12.451

Abstract

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.

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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

Information

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

zbMATH: 07033141
MathSciNet: MR3905340
Digital Object Identifier: 10.2140/involve.2019.12.451

Subjects:
Primary: 17B08, 20G05

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 3 • 2019
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