论文标题
舒伯特品种的模棱两可的K理论和切线空间
Equivariant K-theory and tangent spaces to Schubert varieties
论文作者
论文摘要
舒伯特（Schubert）品种的切线空间由Lakshmibai和Seshadri进行特征。 Lakshmibai将此结果扩展到其他经典类型。我们在cominuscule g/p的舒伯特品种中给出了切线空间的统一表征。我们的结果超出了cominuscule g/p；他们描述了xb点g/b中任何舒伯特品种的切线空间，其中x是彼得森（Peterson）的cominuscule weyl ofter元素。我们的结果在任何时候都为任何舒伯特品种提供了有关切线空间的部分信息。我们的方法是描述Kazhdan-Lusztig品种的切线空间，然后恢复Schubert品种的结果。我们的证明使用了各种圆环动作的切线空间的权重与圆环等效性K理论的阶级的因素之间的关系。证明依赖于由于Graham和Willems而导致的schubert班级的公式，以及由于Knutson和Miller而引起的子Word综合体定理。
Tangent spaces to Schubert varieties of type A were characterized by Lakshmibai and Seshadri. This result was extended to the other classical types by Lakshmibai. We give a uniform characterization of tangent spaces to Schubert varieties in cominuscule G/P. Our results extend beyond cominuscule G/P; they describe the tangent space to any Schubert variety in G/B at a point xB, where x is a cominuscule Weyl group element in the sense of Peterson. Our results also give partial information about the tangent space to any Schubert variety at any point. Our method is to describe the tangent spaces of Kazhdan-Lusztig varieties, and then recover results for Schubert varieties. Our proof uses a relationship between weights of the tangent space of a variety with torus action, and factors of the class of the variety in torus equivariant K-theory. The proof relies on a formula for Schubert classes in equivariant K-theory due to Graham and Willems, as well as a theorem on subword complexes due to Knutson and Miller.
