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Toric degenerations of flag varieties from matching field tableaux
Authors:Oliver Clarke  Fatemeh Mohammadi
Institution:1. University of Bristol, School of Mathematics, BS8 1TW, Bristol, UK;2. Department of Mathematics: Algebra and Geometry, Ghent University, 9000 Gent, Belgium;3. Department of Mathematics and Statistics, UiT – The Arctic University of Norway, 9037 Tromsø, Norway;1. Department of Mathematics, Emory University, Atlanta, GA 30322, United States of America;2. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States of America;1. Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil;2. Sobolev Institute of Mathematics, Novosibirsk, Russia;3. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China;1. Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell''Insubria, Via Valleggio 11, 22100 Como, Italy;2. Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Strasse 4, D-24098 Kiel, Germany;3. Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, C/José Antonio Novais 10, 28040 Madrid, Spain;4. Institut für Differentialgeometrie, Gottfried Wilhelm Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany;1. Department of Mathematics, Columbia University, New York, NY 10027, United States of America;2. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of America
Abstract:We present families of tableaux which interpolate between the classical semi-standard Young tableaux and matching field tableaux. Algebraically, this corresponds to SAGBI bases of Plücker algebras. We show that each such family of tableaux leads to a toric ideal, that can be realized as initial of the Plücker ideal, hence a toric degeneration for the flag variety.
Keywords:Toric degenerations  SAGBI bases  Khovanskii bases  Grassmannians  Flag varieties  Semi-standard Young tableaux
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