Vertices of Gelfand--Tsetlin Polytopes
نویسندگان
چکیده
منابع مشابه
Vertices of Gelfand-Tsetlin Polytopes
This paper is a study of the polyhedral geometry of Gelfand–Tsetlin polytopes arising in the representation theory of glnC 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...
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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, name...
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Article history: Received 20 June 2012 Available online 13 February 2013
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For a partition λ = (λ1, . . . , λn), one can construct a Gelfand-Tsetlin polytope GTλ associated to λ. For all GTλ, we give a formula for the diameter of the 1-skeleton and exactly describe the combinatorial automorphism group Aut(GTλ). Letting m be the number of distinct λi, we give an alternate proof of the formula in [GKT13] counting the number of vertices form ≤ 3, and we describe a genera...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-1133-3