Polyhedral realizations of crystal bases and convex-geometric Demazure operators
Polyhedral realizations of crystal bases and convex-geometric Demazure operators
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晶体基和凸几何 Demazure 算子的多面体实现
DOI：
10.1007/s00029-019-0522-7
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Naoki Fujita
中科院分区：
文献类型：
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作者：
Hiraku Abe;Naoki Fujita;and Haozhi Zeng;Naoki Fujita
本文的主要对象是一族有理凸多面体，其格点给出了最高权晶体基的多面体实现。这个族中的每一个多胞形都与旗形簇的牛顿-奥肯科夫体相同，并且它给出环面退化。在本文中，我们证明了在这个家庭中的一个特定类的多面体是由Kiritchenko的Demazure算子的多面体。这意味着这类多面体都是格多面体。作为应用，给出了相应复曲面簇为Gorenstein Fano的一个充分条件.
The main object in this paper is a family of rational convex polytopes whose lattice points give a polyhedral realization of a highest weight crystal basis. Every polytope in this family is identical to a Newton–Okounkov body of a flag variety, and it gives a toric degeneration. In this paper, we prove that a specific class of polytopes in this family is given by Kiritchenko’s Demazure operators on polytopes. This implies that polytopes in this class are all lattice polytopes. As an application, we give a sufficient condition for the corresponding toric variety to be Gorenstein Fano.