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A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical. (English) Zbl 0924.20035
Let \(G\) be a classical algebraic group over an algebraically closed field. The authors classify all instances when a parabolic subgroup \(P\) of \(G\) acts on its unipotent radical \(P_u\), or on \(\mathfrak p_u\), the Lie algebra of \(P_u\), with only a finite number of orbits, and furthermore obtain a combinatorial formula for the number of orbits in the finite cases for general linear groups.

MSC:
20G05 Representation theory for linear algebraic groups
20G15 Linear algebraic groups over arbitrary fields
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