论文标题
用于专门非对称麦克唐纳多项式的仿生剂晶体
Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials
论文作者
论文摘要
我们给出了一个晶体理论证明，非对称麦克唐纳多项式专门为$ t = 0 $是仿射量为affine sagzure字符。我们明确地在SemistArdard钥匙小报上明确构建了仿射剂晶体，从而消除了仿射边缘恢复了作者前面构建的有限调整晶体。我们还通过定义明确的嵌入操作员来实现最高权重模块的过滤，该操作员在字符的层面上与专门的非对称麦克唐纳多项式的诺普和萨希的递归运算符相吻合。因此，我们在A型中进行了组合证明，每个仿制指定模块都承认有限的援助标志。
We give a crystal-theoretic proof that nonsymmetric Macdonald polynomials specialized to $t=0$ are affine Demazure characters. We explicitly construct an affine Demazure crystal on semistandard key tabloids such that removing the affine edges recovers the finite Demazure crystals constructed earlier by the authors. We also realize the filtration on highest weight modules by Demazure modules by defining explicit embedding operators which, at the level of characters, parallels the recursion operators of Knop and Sahi for specialized nonsymmetric Macdonald polynomials. Thus we prove combinatorially in type A that every affine Demazure module admits a finite Demazure flag.
