Alcove Paths and Gelfand–Tsetlin Patterns

In their study of the equivariant K-theory generalized flag varieties G/P, where G is a complex semisimple Lie group, and P parabolic subgroup G, Lenart Postnikov introduced combinatorial tool, called alcove path model. It provides model for highest weight crystals with dominant integral weights, generalizing by semistandard Young tableaux. this paper, we prove simple explicit formula describing crystal isomorphism between Gelfand–Tsetlin pattern type A.