论文标题
Gelfand-tsetlin的组合突变，Feigin-Fourier-Littelmann-Vinberg多面体和块对角线匹配的场多型
Combinatorial Mutations of Gelfand-Tsetlin Polytopes, Feigin-Fourier-Littelmann-Vinberg Polytopes, and Block Diagonal Matching Field Polytopes
论文作者
论文摘要
从代表理论的角度来定义了Gelfand-Tsetlin和Feigin-fourier-littelmann-Vinberg多面体，以使某些基础参数为最高权重的不可减少模块的某些基础。这些多面体是格拉曼尼亚人的牛顿 - 科恩科夫的身体，尤其是GT-Polytope是弦乐多层的一个例子。如Ardila，Bliem和Salaza所示，多面体将组合描述作为斯坦利的秩序和链层。我们证明这些多面体发生在匹配的场多型中。此外，我们表明它们是通过仅通过匹配的磁场来传递的一系列组合突变的相关性。结果，我们获得了一个匹配领域的家族，从而引起了格拉斯曼尼亚人的复曲面变性。此外，家庭中的所有多人都是牛顿 - 科恩科夫的尸体。
The Gelfand-Tsetlin and the Feigin-Fourier-Littelmann-Vinberg polytopes for the Grassmannians are defined, from the perspective of representation theory, to parametrize certain bases for highest weight irreducible modules. These polytopes are Newton-Okounkov bodies for the Grassmannian and, in particular, the GT-polytope is an example of a string polytope. The polytopes admit a combinatorial description as the Stanley's order and chain polytopes of a certain poset, as shown by Ardila, Bliem and Salaza. We prove that these polytopes occur among matching field polytopes. Moreover, we show that they are related by a sequence of combinatorial mutations that passes only through matching field polytopes. As a result, we obtain a family of matching fields that give rise to toric degenerations for the Grassmannians. Moreover, all polytopes in the family are Newton-Okounkov bodies for the Grassmannians.
