Finite type multiple flag varieties of exceptional groups

2017/08/21 by Dan Barbasch, Sérgio Da Silva, Barbasch, Dan +5
Mathematics · Physics and Astronomy · #11S90 #14M15 #22E46 #22E47 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1708.06341

openalex publication_date 2017/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a simple complex Lie group G acting diagonally on a triple flag variety G/P₁× G/P₂× G/P₃, 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 F₄. The E₆, E₇, and E₈ cases will be treated in a subsequent paper.

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