关于B型和C型Mirkovic-Vilonen多面体的Anderson-Mirkovic猜想的修正
A modification of the Anderson-Mirkovic conjecture for Mirkovic-Vilonen polytopes in types B and C
摘要:
本文给出了$B$和$C$型Mirković-Vilonen多面体上的(降)Kashiwara算子的显式描述,为归纳生成Mirković-Vilonen多面体提供了一种简单的方法.这种描述可以被认为是对最初的安德森-米尔科维奇猜想的修改,卡姆尼策在$A$类型的情况下证明了这一猜想,并在$C_{3}$类型的情况下提出了一个反例。
英文摘要:
We give an explicit description of the (lowering) Kashiwara operators on Mirković-Vilonen polytopes in types $B$ and $C$, which provides a simple method for generating Mirković-Vilonen polytopes inductively. This description can be thought of as a modification of the original Anderson-Mirković conjecture, which Kamnitzer proved in the case of type $A$, and presented a counterexample in the case of type $C_{3}$.
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