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2005•St Petersburg Mathematical JournalOpen access

Generation of pairs of short root subgroups in Chevalley groups

V.V. Nesterov

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Abstract

On the basis of the Bruhat decomposition, the subgroups generated by pairs of unipotent short root subgroups in Chevalley groups of type $\mathrm {B}_{\ell }$, $\mathrm {C}_{\ell }$, and $\mathrm {F}_4$ over an arbitrary field are described. Moreover, the orbits of a Chevalley group acting by conjugation on such pairs are classified.

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On the basis of the Bruhat decomposition, the subgroups generated by pairs of unipotent short root subgroups in Chevalley groups of type $\mathrm {B}_{\ell }$, $\mathrm {C}_{\ell }$, and $\mathrm {F}_4$ over an arbitrary field are described. Moreover, the orbits of a Chevalley group acting by conjugation on such pairs are classified.

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Available abstract

On the basis of the Bruhat decomposition, the subgroups generated by pairs of unipotent short root subgroups in Chevalley groups of type $\mathrm {B}_{\ell }$, $\mathrm {C}_{\ell }$, and $\mathrm {F}_4$ over an arbitrary field are described. Moreover, the orbits of a Chevalley group acting by conjugation on such pairs are classified.

Key concepts: Unipotent, Mathematics, Group of Lie type, Root (linguistics), Pure mathematics, Type (biology), Field (mathematics), Decomposition

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