G/B-丛K-理论中的Pieri-Chevalley公式
A Pieri-Chevalley formula in the K-theory of a G/B-bundle
摘要：
这个公告的主要结果是一个公式的张量积类的齐次线丛与舒伯特类，表示为一个K（X）-线性组合的舒伯特类。我们认为这个公式是Schubert类的相交理论中最一般的一致结果：它与Fulton和Lascoux最近给出的GL_n（C）/B-丛的一个类似公式有关。事实上，在这种情况下，他们的公式和我们的一致，一旦知道如何转换之间的组合与tableaux和我们的利特尔曼路径。O. Mathieu也证明了我们的公式所隐含的正性。将陈省身特征标应用到我们的公式中，并使最低阶项相等，我们得到了本文标题中提到的Chevalley经典结果的一个相对版本。
英文摘要：
The main result of this announcement is a formula for the tensor product of the class of a homogeneous line bundle with a Schubert class, expressed as a K(X)-linear combination of Schubert classes. We believe that this formula is the most general uniform result in the intersection theory of Schubert classes: it is related to a recent result of Fulton and Lascoux who presented a similar formula for a GL_n(C)/B-bundle. Indeed, in this case, their formula and ours coincide once one knows how to translate between their combinatorics with tableaux and ours with Littelmann paths. O. Mathieu has also proved the positivity which is implied by our formula. Applying the Chern character to our formula, and equating the lowest order terms we obtain a relative version of the classical result of Chevalley alluded to in the title of this paper.
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