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Polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal |
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| Authors: | Syu Kato Satoshi Naito Daisuke Sagaki |
| Institution: | aDepartment of Mathematics, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan;bInstitute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan |
| Abstract: | In this paper, we give a polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal in terms of Minkowski sums of extremal Mirkovi?–Vilonen polytopes. As an immediate consequence of this result, we provide a necessary (but not sufficient) polytopal condition for a Mirkovi?–Vilonen polytope to lie in a Demazure crystal. |
| Keywords: | Quantum group Crystal basis Crystal Mirkovi?&ndash Vilonen polytope Mirkovi?&ndash Vilonen cycle Demazure module Demazure crystal |
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