Finite type multiple flag varieties of exceptional groups

Abstract

Consider a simple complex Lie group G acting diagonally on a triple flag variety G/P 1 × G/P 2 × 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.

Multiple flag ind-varieties with finitely many orbits

“…If no factor X i is a full flag variety, the problem is considered in the classical cases in [7,8] (types A and C, through the theory of quiver representations) and in [9,10] (types B and D). For exceptional groups, the general question has been considered in [1].…”

“…Acknowledgement. We are thankful to Roman Avdeev for pointing out the papers [1] and [10] to us, and for some constructive remarks. We thank Alan Huckleberry for a general discussion of the topic of this work.…”