We study the tropicalization of symplectic flag varieties with respect to the Plücker embedding. We identify a particular maximal prime cone in this tropicalization by explicitly giving its facets. For every interior point of this maximal cone, the corresponding Gröbner degeneration is the toric variety associated to the Feigin-Fourier-Littelmann-Vinberg (FFLV) polytope. Our main tool is the notion of birational sequences introduced by Fourier, Littelmann and the second author, which bridges between weighted PBW filtrations of representations of symplectic Lie algebras and degree functions on defining ideals of symplectic flag varieties.
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Balla et al. (2024) studied this question.
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