Vol. 12, No. 3, 2019

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

Madeleine Burkhart and David Vella

Vol. 12 (2019), No. 3, 451–462
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 An for n 4, and when G is type B2. We elaborate on this work in the case when G = SO5(k) (type B2) 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 An, can be approached the same way and are treated in a separate paper.

Keywords
nilpotent orbits, Borel subgroups, modality
Mathematical Subject Classification 2010
Primary: 17B08, 20G05
Milestones
Received: 16 August 2017
Revised: 8 February 2018
Accepted: 10 July 2018
Published: 14 December 2018

Communicated by Kenneth S. Berenhaut
Authors
Madeleine Burkhart
Mathematics Department
University of Washington
Seattle, WA
United States
David Vella
Mathematics and Statistics Department
Skidmore College
Saratoga Springs, NY
United States