A Sufficient Condition for a Hibi Ring to Be Level and Levelness of Schubert Cycles |
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| Authors: | Mitsuhiro Miyazaki |
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| Institution: | 1. Department of Mathematics , Kyoto University of Education , Fukakusa-Fujinomori-cho, Fushimi-ku, Kyoto, Japan g53448@kyokyo-u.ac.jp |
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| Abstract: | Let K be a field, D a finite distributive lattice and P the set of all join-irreducible elements of D. We show that if {y ∈ P | y ≥ x} is pure for any x ∈ P, then the Hibi ring ? K (D) is level. Using this result and the argument of sagbi basis theory, we show that the homogeneous coordinate rings of Schubert subvarieties of Grassmannians are level. |
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| Keywords: | Hibi ring Level ring Sagbi basis Schubert subvariety |
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