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Finite, tame, and wild actions of parabolic subgroups in \(\text{GL}(V)\) on certain unipotent subgroups. (English) Zbl 0968.20023
A parabolic subgroup of \(\text{GL}(V)\) is the stabilizer of a (possibly incomplete) flag of subspaces of \(V\). If \(P\) is such a parabolic subgroup, the authors study the action of \(P\) on the Lie algebra of its unipotent radical and more generally on the \(l\)-th term of the descending central series. They characterize the cases where this action has a finite number of orbits.
The proof relies on seeing the orbits as isomorphism classes of some category, which is then shown to be equivalent to a category of modules over an algebra.

20G05 Representation theory for linear algebraic groups
Full Text: DOI
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