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One approach to Schubert calculus is to realize Schubert classes as concretecombinatorial objects such as Schubert polynomials. Through an identificationof the cohomology ring of the type A full flag variety with the polytope ringof the Gelfand-Tsetlin polytopes, Kiritchenko-Smirnov-Timorin realized eachSchubert class as a sum of reduced (dual) Kogan faces. In this paper, weexplicitly describe string parametrizations of opposite Demazure crystals,which give a natural generalization of reduced dual Kogan faces. We also relatereduced Kogan faces with Demazure crystals using the theory of mitosisoperators, and apply these observations to develop the theory of Schubertcalculus on symplectic Gelfand-Tsetlin polytopes.

Schubert calculus from polyhedral parametrizations of Demazure crystals