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