模式图的上同调结果
Cohomological consequences of the pattern map
摘要：
Billey和Braden定义了旗流形上的映射，它们是置换模式的几何对应。他们的模式图的一部分是一个嵌入的旗流形的列维子群到全旗流形。给出了诱导映射上同调的两个表达式。一个是关于生成元的，另一个是关于舒伯特基的。我们表明，在第二个表达式中的系数自然舒伯特结构常数，因此积极的。这些公式也适用于K-理论，并推广了已知的上同调和K-理论的A型公式。
英文摘要：
Billey and Braden defined maps on flag manifolds that are the geometric counterpart of permutation patterns. A section of their pattern map is an embedding of the flag manifold of a Levi subgroup into the full flag manifold. We give two expressions for the induced map on cohomology. One is in terms of generators and the other is in terms of the Schubert basis. We show that the coefficients in the second expression are naturally Schubert structure constants and therefore positive. These formulas also hold for K-theory, and generalize known formulas in type A for cohomology and K-theory.
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