# Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann polytopes as marked poset polytopes - Mathematics > Combinatorics

Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann polytopes as marked poset polytopes - Mathematics > Combinatorics - Download this document for free, or read online. Document in PDF available to download.

Abstract: Stanley 1986 showed how a finite partially ordered set gives rise to twopolytopes, called the order polytope and chain polytope, which have the sameEhrhart polynomial despite being quite different combinatorially. We generalizehis result to a wider family of polytopes constructed from a poset P withintegers assigned to some of its elements.Through this construction, we explain combinatorially the relationshipbetween the Gelfand-Tsetlin polytopes 1950 and the Feigin-Fourier-Littelmannpolytopes 2010, which arise in the representation theory of the speciallinear Lie algebra. We then use the generalized Gelfand-Tsetlin polytopes ofBerenstein and Zelevinsky 1989 to propose conjectural analogues of theFeigin-Fourier-Littelmann polytopes corresponding to the symplectic and oddorthogonal Lie algebras.

Author: ** Federico Ardila, Thomas Bliem, Dido Salazar**

Source: https://arxiv.org/