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• W2083421159 abstract "This paper is a study of the polyhedral geometry of Gelfand–Tsetlin polytopes arising in the representation theory of ${frak gl}_n Bbb C$ and algebraic combinatorics. We present a combinatorial characterization of the vertices and a method to calculate the dimension of the lowest-dimensional face containing a given Gelfand–Tsetlin pattern. As an application, we disprove a conjecture of Berenstein and Kirillov about the integrality of all vertices of the Gelfand–Tsetlin polytopes. We can construct for each $ngeq5$ a counterexample, with arbitrarily increasing denominators as $n$ grows, of a nonintegral vertex. This is the first infinite family of nonintegral polyhedra for which the Ehrhart counting function is still a polynomial. We also derive a bound on the denominators for the nonintegral vertices when $n$ is fixed." @default.
• W2083421159 created "2016-06-24" @default.
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• W2083421159 date "2004-09-02" @default.
• W2083421159 modified "2023-10-03" @default.
• W2083421159 title "Vertices of Gelfand--Tsetlin Polytopes" @default.
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• W2083421159 doi "https://doi.org/10.1007/s00454-004-1133-3" @default.
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