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arXiv · 1903.08275

Gelfand-Tsetlin polytopes: a story of flow and order polytopes

Ricky Ini Liu·Karola Mészáros·Avery St. Dizier
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Abstract

Gelfand-Tsetlin polytopes are prominent objects in algebraic combinatorics. The number of integer points of the Gelfand-Tsetlin polytope $\mathrm{GT}(λ)$ is equal to the dimension of the corresponding irreducible representation of $GL(n)$. It is well-known that the Gelfand-Tsetlin polytope is a marked order polytope; the authors have recently shown it to be a flow polytope. In this paper, we draw corollaries from this result and establish a general theory connecting marked order polytopes and flow polytopes.

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Ricky Ini Liu, Karola Mészáros, Avery St. Dizier. 2019-03-19. Gelfand-Tsetlin polytopes: a story of flow and order polytopes. https://arxiv.org/abs/1903.08275

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