Weighted PBW degenerations and tropical flag varieties
Xin Fang, Evgeny Feigin, Ghislain Fourier, Igor Yur'evich Makhlin · Communications in Contemporary Mathematics · 2018
We study algebraic, combinatorial and geometric aspects of weighted Poincaré–Birkhoff–Witt (PBW)-type degenerations of (partial) flag varieties in type [Formula: see text]. These degenerations are labeled by degree functions lying in an explicitly defined polyhedral cone, which can be identified with a maximal cone in the tropical flag variety. Varying the degree function in the cone, we recover, for example, the classical flag variety, its abelian PBW degeneration, some of its linear degenerations and a particular toric degeneration.