论文标题
Kohnert的标记Schur模块规则
Kohnert's rule for flagged Schur modules
论文作者
论文摘要
标记的Schur模块在Borel subgerbra的作用下概括了通用线性群的不可约表示。他们的角色包括许多重要的schur多项式概括，例如纽扣字符，标记的偏斜schur多项式和舒伯特多项式。在本文中，我们可以证明，由于Kohnert且仅当索引图位于西北时，因此可以使用简单的组合算法来计算标记的Schur模块的字符。这给出了一个新的证据，表明标记的Schur模块的字符是纽扣字符的非负和总和，并为Kohnert多项式提供了代表理论解释。
Flagged Schur modules generalize the irreducible representations of the general linear group under the action of the Borel subalgebra. Their characters include many important generalizations of Schur polynomials, such as Demazure characters, flagged skew Schur polynomials, and Schubert polynomials. In this paper, we prove the characters of flagged Schur modules can be computed using a simple combinatorial algorithm due to Kohnert if and only if the indexing diagram is northwest. This gives a new proof that characters of flagged Schur modules are nonnegative sums of Demazure characters and gives a representation theoretic interpretation for Kohnert polynomials.
