Adjoint action of automorphism groups of projective representations of Dynkin quivers

Details Adjoint action of automorphism groups of projective representations of Dynkin quivers Adjoint action of automorphism groups of projective representations of Dynkin quivers

2010-02-23

arxiv.org/abs/1002.4432v2

Mathematics

Representation Theory

Scientific paper

Let $\Delta$ be a quiver and let $P$ be a projective representation of $\Delta$. We study the adjoint action of $Aut P$ on the space of radical endomorphisms and show that there is a dense open orbit for all $P$, if and only if $\Delta$ is a Dynkin quiver. Our main application is to show the existence of dense open orbits for the adjoint action of subgroups of parabolics in $Gl_n$ on the nilpotent radical of corresponding subalgebras.

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