Small toric resolutions of toric varieties of string polytopes with small indices

Let G be a semisimple algebraic group over [Formula: see text]. For reduced word text] of the longest element in Weyl and dominant integral weight text], one can construct string polytope whose lattice points encode character irreducible representation The is singular general combinatorics polytopes heavily depends on choice In this paper, we study when present sufficient condition such that toric variety has small resolution. Indeed, indices regular, explicitly resolution using Bott manifold. Our main theorem implies any admits As byproduct, show if then for which particular anticanonical limit partial flag Gorenstein Fano. Furthermore, apply our result to symplectic topology full manifold obtain formula disk potential Lagrangian torus fibration obtained from flat degeneration