论文标题
Kazhdan-Lusztig Schubert的几何特性基础
Geometric properties of the Kazhdan-Lusztig Schubert basis
论文作者
论文摘要
我们研究由Hecke代数的Kazhdan-Lusztig在$ k $ - 理论和双曲线共同体学理论中确定的。我们首先表明，在$ k $的理论中，Kazhdan-Lusztig基地的两个不同选择产生了双基础，其中一个可以解释为交叉杂种混合Hodge模块的特征类别。在模棱两可的双曲线共同体中，我们表明，如果舒伯特的品种平滑，那么它决定的类别与kazhdan-lusztig的类别相吻合。这被称为平滑度猜想。对于格拉斯曼尼亚人来说，我们证明了Kazhdan-Lusztig的阶级与Zelevinsky的小决议确定的类别相吻合。所谓的KL-Schubert基础的这些特性表明，它是与Schubert的现有类似物的基础，这是双曲线共同体的基础。后者是对更通用的椭圆共同体的非常有用的测试。
We study classes determined by the Kazhdan-Lusztig basis of the Hecke algebra in the $K$-theory and hyperbolic cohomology theory of flag varieties. We first show that, in $K$-theory, the two different choices of Kazhdan-Lusztig bases produce dual bases, one of which can be interpreted as characteristic classes of the intersection homology mixed Hodge modules. In equivariant hyperbolic cohomology, we show that if the Schubert variety is smooth, then the class it determines coincides with the class of the Kazhdan-Lusztig basis; this was known as the Smoothness Conjecture. For Grassmannians, we prove that the classes of the Kazhdan-Lusztig basis coincide with the classes determined by Zelevinsky's small resolutions. These properties of the so-called KL-Schubert basis show that it is the closest existing analogue to the Schubert basis for hyperbolic cohomology; the latter is a very useful testbed for more general elliptic cohomologies.
