Irreducible subgroups generated by root subgroups in the group SL(𝑛,𝐾)
https://doi.org/10.22405/2226-8383-2025-26-4-123-138
Abstract
In the present paper we give a new proof of the description of irreducible subgroups generated by root subgroups in special linear group SL(𝑛,𝐾). For the first time such a description was
appeared in J. McLaughlin’s work. His work was one of the first papers dedicated to study of the generations by long root unipotent subgroups in Chevalley groups. At the present time the geometry of long root subgroups is a well-established field. But it remains a lot of unsolved tasks about short root unipotent subgroups. In particular, the description of irreducible subgroups
generated by short root subgroups in exceptional Chevalley groups over arbitrary field is unknown. In our proof we consider the group SL(𝑛,𝐾) as the Chevalley group of type Aℓ. Thus
in our opinion it is possible to use the given approach for study of the irreducible subgroups generated by short root subgroups in Chevalley groups.
About the Authors
Maksim Andreevich Kandinskiy
Saint Petersburg State University
Russian Federation
Russian Federation
postgraduate student
Vladimir Vicktorovich Nesterov
Saint Petersburg State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
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Review
For citations:
Kandinskiy M.A., Nesterov V.V. Irreducible subgroups generated by root subgroups in the group SL(𝑛,𝐾). Chebyshevskii Sbornik. 2025;26(4):123-138. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-123-138
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