Toric degenerations of flag varieties from matching field tableaux

Abstract

We present families of tableaux which interpolate between the classical semi-standard Young tableaux and matching field tableaux. Algebraically, this corresponds to SAGBI bases of Plücker algebras. We show that each such family of tableaux leads to a toric ideal, that can be realized as initial of the Plücker ideal, hence a toric degeneration for the flag variety.