Finite type multiple flag varieties of exceptional groups

Dan Barbasch; Sergio Da Silva; Balázs Elek; Gautam Gopal Krishnan

Finite type multiple flag varieties of exceptional groups

Representation Theory 2017-08-22 v1 Algebraic Geometry

Authors: Dan Barbasch , Sergio Da Silva , Balázs Elek , Gautam Gopal Krishnan

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.

Keywords

finite group theory nilpotent orbits flag varieties

Cite

@article{arxiv.1708.06341,
  title  = {Finite type multiple flag varieties of exceptional groups},
  author = {Dan Barbasch and Sergio Da Silva and Balázs Elek and Gautam Gopal Krishnan},
  journal= {arXiv preprint arXiv:1708.06341},
  year   = {2017}
}

Comments

11 pages, Sage code included in ancillary file

Finite type multiple flag varieties of exceptional groups

Abstract

Keywords

Cite

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