Federico Ardila ; Thomas Bliem ; Dido Salazar - Gelfand―Tsetlin Polytopes and Feigin―Fourier―Littelmann―Vinberg Polytopes as Marked Poset Polytopes

dmtcs:2888 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2888
Gelfand―Tsetlin Polytopes and Feigin―Fourier―Littelmann―Vinberg Polytopes as Marked Poset Polytopes

Authors: Federico Ardila ; Thomas Bliem ; Dido Salazar

    Stanley (1986) showed how a finite partially ordered set gives rise to two polytopes, called the order polytope and chain polytope, which have the same Ehrhart polynomial despite being quite different combinatorially. We generalize his result to a wider family of polytopes constructed from a poset P with integers assigned to some of its elements. Through this construction, we explain combinatorially the relationship between the Gelfand–Tsetlin polytopes (1950) and the Feigin–Fourier–Littelmann–Vinberg polytopes (2010, 2005), which arise in the representation theory of the special linear Lie algebra. We then use the generalized Gelfand–Tsetlin polytopes of Berenstein and Zelevinsky (1989) to propose conjectural analogues of the Feigin–Fourier–Littelmann–Vinberg polytopes corresponding to the symplectic and odd orthogonal Lie algebras.


    Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
    Section: Proceedings
    Published on: January 1, 2011
    Imported on: January 31, 2017
    Keywords: poset,polytope,semisimple Lie algebra,PBW filtration,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • Creating Momentum through Communicating Mathematics; Funder: National Science Foundation; Code: 0841164
    • Combinatorics in Geometry; Funder: National Science Foundation; Code: 0801075
    • CAREER: Matroids, polytopes, and their valuations in algebra and geometry; Funder: National Science Foundation; Code: 0956178

    Linked data

    Source : ScholeXplorer HasVersion ARXIV 1008.2365
    Source : ScholeXplorer HasVersion DOI 10.48550/arxiv.1008.2365
    • 10.48550/arxiv.1008.2365
    • 1008.2365
    Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann polytopes as marked poset polytopes
    Ardila, Federico ; Bliem, Thomas ; Salazar, Dido ;

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