Gelfand-Tsetlin polytopes and the integer decomposition property

Let P be the Gelfand–Tsetlin polytope defined by the skew shape λ/μ and weight w. In the case corresponding to a standard Young tableau, we completely characterize for which shapes λ/μ the polytope P is integral. Furthermore, we show that P is a compressed polytopewhenever it is integral and corresponds to a standard Young tableau.We conjecture that a similar property holds for arbitraryw, namely thatP has the integer decomposition property whenever it is integral. Finally, a natural partial ordering onGT-polytopes is introduced that provides information about integrality and the integer decomposition property, which implies the conjecture for certain shapes. © 2015 Elsevier Ltd. All rights reserved.