Finite type multiple flag varieties of exceptional groups
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 clas...
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| creator | Barbasch, Dan Da Silva, Sergio Elek, Balázs Krishnan, Gautam Gopal |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1708.06341 |
| format | Article |
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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
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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
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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
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| subjects | Mathematics - Algebraic Geometry Mathematics - Representation Theory |
| title | Finite type multiple flag varieties of exceptional groups |
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