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arXiv · 1708.06341

Finite type multiple flag varieties of exceptional groups

Dan Barbasch·Sergio Da Silva·Balázs Elek·Gautam Gopal Krishnan
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Abstract

Consider a simple complex Lie group $G$ acting diagonally on a triple flag variety $G/P_1\times G/P_2\times G/P_3$, where $P_i$ is parabolic subgroup of $G$. We provide an algorithm for systematically checking when this action has finitely many orbits. We then use this method to give a complete classification for when $G$ is of type $F_4$. The $E_6, E_7,$ and $E_8$ cases will be treated in a subsequent paper.

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Dan Barbasch, Sergio Da Silva, Balázs Elek, Gautam Gopal Krishnan. 2017-08-21. Finite type multiple flag varieties of exceptional groups. https://arxiv.org/abs/1708.06341

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