论文标题
链订购的多面体：复式退化，年轻的tableaux和单基碱基
Chain-order polytopes: toric degenerations, Young tableaux and monomial bases
论文作者
论文摘要
我们的第一个结果意识到了Gelfand-tsetlin Poset的每个标记链级多层（MCOP）的复合品种，作为标志品种的显式Gröbner（Sagbi）变性。这概括了sturmfels/gonciulea--lakshmibai/kogan-麦格尔 - 麦格尔构建，用于gelfand-tsetlin变性为MCOP设置。我们方法的关键思想是利用烟斗梦想定义plücker坐标中曲折品种的实现。然后，我们使用这种方法将两种更知名的构造推广到任意MCOPS：标准的单一理论，例如Semistandard Young Tableaux和PBW Monomial bases提供的标准理论，例如FFLV碱基等不可减至的表示。在附录中，我们介绍了半无限管道梦的概念，并使用它来获得无限的poset polytopes家族，每个家族都提供了半无限grassmannian的复曲面变性。
Our first result realizes the toric variety of every marked chain-order polytope (MCOP) of the Gelfand--Tsetlin poset as an explicit Gröbner (sagbi) degeneration of the flag variety. This generalizes the Sturmfels/Gonciulea--Lakshmibai/Kogan--Miller construction for the Gelfand--Tsetlin degeneration to the MCOP setting. The key idea of our approach is to use pipe dreams to define realizations of toric varieties in Plücker coordinates. We then use this approach to generalize two more well-known constructions to arbitrary MCOPs: standard monomial theories such as those given by semistandard Young tableaux and PBW-monomial bases in irreducible representations such as the FFLV bases. In an addendum we introduce the notion of semi-infinite pipe dreams and use it to obtain an infinite family of poset polytopes each providing a toric degeneration of the semi-infinite Grassmannian.
