论文标题
kohnert多项式的项
Demazure crystals for Kohnert polynomials
论文作者
论文摘要
Kohnert多项式是由作者和Searles先前定义的第一个象限中的单位细胞图索引的多项式，这些象限和Searles定义了schubert多项式群和一般线性群的共同概括。氮杂晶体是正常晶体的某些截断，其角色是扎唑角色。对于满足西南条件的每个图，我们构建了一个摘要晶体，其特征是给定图的Kohnert多项式，解决了作者和Searles的较早猜想，这些多项式将这些多项式非确定地扩展到Demazure字符中。我们为扩展提供了明确的公式，其中包括对相应的Kohnert多项式为单一的调整特征的那些图表的表征。
Kohnert polynomials are polynomials indexed by unit cell diagrams in the first quadrant defined earlier by the author and Searles that give a common generalization of Schubert polynomials and Demazure characters for the general linear group. Demazure crystals are certain truncations of normal crystals whose characters are Demazure characters. For each diagram satisfying a southwest condition, we construct a Demazure crystal whose character is the Kohnert polynomial for the given diagram, resolving an earlier conjecture of the author and Searles that these polynomials expand nonnegatively into Demazure characters. We give explicit formulas for the expansions with applications including a characterization of those diagrams for which the corresponding Kohnert polynomial is a single Demazure character.
