论文标题
重量多面体和项的饱和度
Weight polytopes and saturation of Demazure characters
论文作者
论文摘要
对于$ g $，还原组和$ t \ subset b $ A最大圆环和Borel子组，纽扣模块是某些$ b $ - submodules，由Weyl Group的元素，有限的不可列出表示$ G $的元素索引。为了描述在调整模块中出现的$ t $加权空间，我们研究了这些权重的凸壳 - 纽扣多层。我们通过顶点和不等式来表征这些多面体，并使用这些结果证明纽扣字符已饱和，而对于$ g $来说是经典的谎言类型的简单。专门为$ g = gl_n $，我们恢复了Fink，Mészáros和St. Dizier的结果，以及在关键的多项式上分别粉丝和Guo，最初由Monical，Tokcan和Yong猜想。
For $G$ a reductive group and $T\subset B$ a maximal torus and Borel subgroup, Demazure modules are certain $B$-submodules, indexed by elements of the Weyl group, of the finite irreducible representations of $G$. In order to describe the $T$-weight spaces that appear in a Demazure module, we study the convex hull of these weights - the Demazure polytope. We characterize these polytopes both by vertices and by inequalities, and we use these results to prove that Demazure characters are saturated, in the case that $G$ is simple of classical Lie type. Specializing to $G=GL_n$, we recover results of Fink, Mészáros, and St. Dizier, and separately Fan and Guo, on key polynomials, originally conjectured by Monical, Tokcan, and Yong.
