Gelfand-Tsetlin polytopes and the integer decomposition property

Abstract

Let $P$ be the Gelfand--Tsetlin polytope defined by the skew shape $\lambda /\mu$ and weight $w$. In the case corresponding to a standard Young tableau, we completely characterize for which shapes $\lambda /\mu$ the polytope $P$ is integral. Furthermore, we show that $P$ is a compressed polytope whenever it is integral and corresponds to a standard Young tableau. We conjecture that a similar property hold for arbitrary $w$, namely that $P$ has the integer decomposition property whenever it is integral. Finally, a natural partial ordering on GT-polytopes is introduced that provides information about integrality and the integer decomposition property, which implies the conjecture for certain shapes.

23 pages. Accepted for publication in the European Journal of Combinatorics

References in corpus (1)

• Existence of unimodular triangulations - positive results

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