algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety Kashiwara crystals; crystals of tableaux; Stembridge crystals; virtual, fundamental, normal crystals; insertion algorithms; plactic monoid; bicrystals and Littlewood-Richardson rule; crystals for Stanley symmetric functions; patterns; Weyl group action; Demazure crystals; crystals and tropical geometry; Lie algebras; representations 